We have performed a set of ab initio calculations of the ground state energy as a function of volume, elastic properties, and phonon spectra of tin selenide in its various crystalline modifications. Based on the obtained data set, the potential of interatomic interaction of SnSe is constructed using the atomic cluster expansion (ACE) method. The potential is further used to study the temperature dependences of thermal and elastic properties of SnSe in the framework of quasi-harmonic approximation.