Simulation of the transient motion of pigs through liquid and gas pipelines is presented. The differential form of the mass and linear momentum equations for compressible liquid and gas flows were solved by a finite difference numerical technique. The fluid flow equations were combined with a linear momentum equation for the pig and a model for bypass flow through the pig. The pig/wall contact forces were simulated by a stick/slip model. The contact forces developed by disk pigs and the pipe wall were predicted by a postbuckling finite element analysis of the discs. Test cases representing typical pigging operations were studied using the numerical model developed. The fluid flow, and pig behavior predicted by the model presented a reasonable behavior, and contributed for a better understanding of the pig dynamics through gas and liquid pipelines.