A local damage model is proposed for the numerical assessment of the static performance of Adobe masonry components. The model was applied to simulate the experimental behaviour of sundried soil bricks and mud mortar tested in uniaxial compression and bending. Numerical simulations of the model are made mesh objective by means of a rate dependent regularization algorithm in statics. This is achieved using a generalization of the damage delay concept based on a decomposition of the Dirichlet boundary condition. It allows non-dimensionality of model parameters mathematically needed to prevent loss of ellipticity of the equilibrium equations of the model. The entire regularization algorithm is integrated within an implicit Newton-Raphson solver.