The deformation of droplets dispersed in a liquid in a cylindrical tube is of great importance to characterize the rheological behavior in the polymer processing. Research on to two phase flows employing the boundary element method (BEM) is abundant. However, in order to simulate the non-Netwonian flow of the two-phase polymeric mixture a finite element method should be employed. In this regard, numerical analysis programs were developed via the finite element method by means of the penalty function considering the interfacial valence condition of the two-phase flow. In addition, moving boundaries between the medium and the droplet were solved via the auto-remeshing technique. The present paper presents detailed numerical methods together with the auto-remeshing generation and discusses essential numerical results. The proper generation of auto-remeshing was proved to be crucial to obtain the accurate and stable numerical solutions for two-phase flows and the results obtained by our numerical methods were in good agreement with the previous results by BEM in the literature. The present work can be applicable to the study of the deformation characteristics for complex systems frequently encountered in polymer blending.