Galappatty attended Dikwella Central College and Matara Rahula College. In 1952, he entered University of Ceylon, Peradeniya campus, to study for a bachelor's degree in economics. At Peradeniya, he started associating with Professor Ediriweera Sarachchandra and Charles Silva and was involved in theatre work.
He was a teacher at Kotte Ananda Sastralaya in 1955 and next joined for a while the State Language Department as a translator, again continuing as a teacher.[3]
From Yale, he went to Broadway in 1959, the first Sri Lankan to work there as well as in off-Broadway productions. During this time, he came under the influence of the Method school, the American offshoot of Konstantin Stanislavski's approach to acting and stagecraft. He worked under two distinguished teachers, Herbert Berghoff and Uta Hagen. He acted in and co-produced two Broadway dramas, Tea House of the August Moon and The Marriage-Go-Round.
He then traveled to many countries, including Spain, Japan and Russia, to study various drama styles and methods. He admired Spain's Federico García Lorca and spent a few weeks experiencing Lorca productions such as Yerma. In Japan, he studied traditional kabuki drama and was involved in a popular production, The Father.
Returning to Sri Lanka in 1961, Galappatty resumed his theatre work. Abandoning the operatic form modelled on Charles Silva and Sarachhandra crystallization of the Nadagam, he branched out on a new line which tried to fuse the inner-directed acting style that he had imbibed in Broadway with the non-naturalistic native tradition. In 1962, he produced a milestone in Sri Lankan theatre, Muduputtu (Sons of the Seas), showing that the traditional stylistic theatre could be blended very effectively with western realistic technique. Following this, he was at the forefront of Sri Lankan theatre and his productions launched the careers of many talented actors. He was called upon to represent Sri Lanka at United Nations conferences and other international activities.