This paper studies the pressure-induced polygonization of filled multiwall carbon nanotubes (MWNTs). The analysis is based on a multiple-elastic shell model, which assumes that each of the concentric tubes of a MWNT is an individual elastic shell and the adjacent tubes are coupled through van der Waals (vdW) interaction. Here the influence of the filling substances inside MWNTs is modeled as uniformly distributed internal pressure and the attention is focused on the effect of internal pressure on polygonization of MWNTs due to external pressure. The critical values of polygonization pressures are computed numerically with various internal-to-external pressure ratios. In particular, the critical polygonization pressures predicted by the multiple-elastic shell model is in good agreement with known experiment results.