* Prays for those affected by "this great national disaster"
* Elderly poverty, income inequality blights rapid progress
* Fog forces pope to take high-speed train to event
* Catholic Church growing rapidly in South Korea (Adds prayer for ferry victims at end of Mass)
By Philip Pullella and Kahyun Yang
DAEJEON, South Korea, Aug 15 (Reuters) - Pope Francis on Friday commemorated the more than 300 people killed in a ferry disaster in April, and called on South Koreans, among Asia's richest people, to beware of the spiritual "cancer" that often accompanies affluent societies.
On the second day of his first trip to Asia, the pope met with families of victims and some survivors of the tragedy ahead of a Mass before about 50,000 people at the World Cup stadium in the central city of Daejeon.
Hundreds of trees were decked with yellow ribbons in the city in remembrance of those, mostly school children, who died when the Sewol ferry, structurally defective and heavily overloaded, capsized and sank on a routine journey on April 16.
Lee Ho-Jin, the father of one of the victims, and who had been preparing to convert, asked the pope to be baptised into the Catholic Church. The pope said yes and the pontiff will perform the rite himself in Seoul on Saturday, a spokesman said.
At the end of the Mass, Francis prayed for the dead, survivors and relatives of victims of "this great national disaster".
"May this tragic event which has brought all Koreans together in grief confirm their commitment to work together in solidarity for the common good," Francis said.
Earlier, in the homily of the Mass, the pope urged listeners to "combat the allure of a materialism that stifles authentic spiritual and cultural values and the spirit of unbridled competition which generates selfishness and strife".
He said they should see their faith as an "antidote to the spirit of despair that seems to grow like a cancer in societies which are outwardly affluent, yet often experience inner sadness and emptiness".
Rapid economic growth has driven South Korea from the poverty of the aftermath of the 1950-1953 Korean war into the ranks of the world's richest nations, but deepened inequalities. Today, nearly half of the country's elderly are still impoverished.
Francis has made caring for the poor a central theme of his pontificate.
Instead of flying by helicopter as planned, the pope took a high-speed train, due to fog in the Daejeon area. Two carriages were reserved for the papal party and a witness said the pope greeted other passengers when he arrived at the Daejeon station, roughly 140 km (85 miles) south of Seoul.
Francis was greeted at the stadium by a festive crowd, with many in attendance wearing cardboard hats with the words "Viva il Papa, Francesco!" and an image of the pope. Some made a heart shape with their arms as TV cameras focused on them.
The Catholic Church has been growing rapidly in South Korea, doubling in the past 25 years to about 11 percent of the population and adding some 100,000 new members every year.
WEALTH AND INEQUALITY
While outwardly successful and home to some of the world's biggest companies, such as Samsung Electronics Co Ltd and Hyundai Motor Co, South Korean society has become more unequal as its economy has grown.
South Korea is now the 29th richest country in the world in terms of gross domestic product per capita, but many of the graduates that its universities churn out each year struggle to find decent jobs, settling for lower-paying temporary work.
While parents spend thousands of dollars on private tuition to give their children an academic edge, nearly half of elderly South Koreans are impoverished, giving the country the highest poverty rate for senior citizens among the 30 members of the Organization for Economic Cooperation and Development.
Francis made an apparent reference to the polarisation caused by income inequality when he urged his listeners to "reject inhumane economic models which create new forms of poverty and marginalise workers".
Last year, in the first major written work of his papacy, Francis, the first non-European pontiff in 1,300 years, attacked unfettered capitalism as "a new tyranny," urging global leaders to fight poverty and growing inequality.
Francis urged Catholics "to be a generous force for spiritual renewal at every level of society".
The pope began his five-day trip to South Korea on Thursday. The main purpose of the trip is to preside at a gathering of Asian Catholic youth and beatify 124 people killed for their faith in the 18th century. (Additional reporting by Ju-min Park; Editing by Tony Munroe and Jeremy Laurence)