In this work, a plasticity based composite interface model is proposed for failure analysis of unreinforced masonry. The hyperbolic composite interface model consists of a single surface yield criterion, which is a direct extension of Mohr-Coulomb criteria with cut in tension region and a cap in compression region. The inelastic behaviour includes potential crack, slip, and crushing of the masonry joints. A micro mechanical based approach is adopted for failure modelling of the masonry. The model is developed by using a fully implicit backward-Euler integration strategy. It is combined with a local/global Newton solver, based on a consistent tangent operator compatible with an adaptive sub stepping strategy. The model is implemented in standard finite element software (ABAQUS) by using user defined subroutine and verification is conducted in all its basic modes. Finally, the model is validated by comparing with experimental results available in the literature. © 2014 Elsevier Ltd.