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In the present paper, the TFA homogenization procedure is extended to the case of nonuniform eigenstrain in the inclusions, in order to deduce the overall response of regular masonry arrangements to be used for the multiscale analysis of masonry walls. Special constitutive laws, based on damage and plasticity models, are adopted for the mortar. Nonlinear behavior is considered even for some subsets of the blocks; in fact, nonlinear damage and plasticity effects are introduced in the subsets of the block aligned with the head mortar joints. Numerical examples of homogenization are carried out, comparing the nonlinear mechanical response of the masonry obtained performing the proposed homogenization technique with the results recovered by evolutive nonlinear finite element analyses