The `tyssue` Python library seeks to provide a unified interface to implement bio-mechanical models of living tissues. Its main focus is on vertex based epithelium models. `tyssue` allows to model the mechanical behavior of 2D, apical 3D or full 3D epithelia based on the numerical resolution of the equations of motion for the mesh vertices. Biological processes are modeled through changes in the topological and dynamical properties of the mesh. `tyssue` is a modular library. Starting with the same tissue geometry, the choice of constraints, energy potential terms and parameters increases the possibility to answer different biological questions and easily explore mechanical hypotheses.