Based on of Frenkel’s viscose flow approach [1] and Mackenzie and Shuttleworth [2] extension considering trapped gas, a model for the shrinkage of a gaseous pore in a viscoelastic melt driven by surface tension was developed. The viscoelastic flow of polymeric materials was considered by using a simple viscoelastic model described by Bellehumeur [3]. In the simulation the viscoelastic relaxation has a pronounced effect on the time scales of the shrinkage, but does not alter the final equilibrium gas sphere diameter. First attempts at including gas diffusion motivated by the works of Kontopoulou and Vlachopoulos [4] and Gogos [5] will be given. Numerical solutions using our simplified model show, that the inclusion of gas diffusion leads to a complete collapse of the pore. The rate of diffusion can change the time dependence of the collapse mechanism tremendously. [1] Frenkel, Journal of Physics, vol. IX, no. 5, pp. 385-391, 1945. [2] Mackenzie and Shuttleworth, Proc. Phys. Soc. B, vol. 62, p. 833, 1949. [3] Bellehumeur, Kontopoulou and Vlachopoulos, Rheologica Acta, vol. 37, no. 3, pp. 270-278, 1998. [4] Gogos, POLYMER ENGINEERING AND SCIENCE, vol. 44, no. 2, pp. 388-394, 2004. [5] Kontopoulou und Vlachopoulos, POLYMER ENGINEERING AND SCIENCE, Bd. 39, Nr. 7, pp. 1189-1198, 1999.