The asymptotic discrete expansion method is used to construct the initial yield surface of periodic 2D trusses of beams and the evolution of the yield surface with ongoing hardening. It allows simulating the elastoplastic homogenized response of such lattices subjected to multiaxial loadings. The proposed methodology is quite general, as the representative unit cell includes internal nodes and no assumption of uniform deformation is needed. We determined the effective elastoplastic response for the case of stretching dominated lattices without considering bending effects. This methodology has been implemented in algorithmic format in a dedicated code as a user oriented subroutine in finite element calculations, allowing the analysis of a large variety of new 2D lattices. Applications to the conceived Octagon-Mixed, asymmetric and star-square lattices illustrate the powerfulness of the proposed method. The homogenized stress–strain evolutions over loading unloading uniaxial and biaxial cycles are in good agreement with those obtained by finite element simulations performed over complete 2D lattices.