Summary In the present paper, a constitutive viscoelastic model for periodic masonry structures is proposed. Using a dynamic homogenization approach of the continuous and discrete‐based model leads to the determination of the anisotropic material properties by assigning the fictitious stress and strains of the homogeneous cell masonry unit. These properties are defined as complex moduli, which consist of real parts representing elastic stiffness and imaginary ones referring to energy dissipations. The advantage of the proposed model is that the damping properties associated to different modes of vibrations can be easily evaluated. Numerical and parametric investigations are conducted that reveal the capabilities of the model to an accurate prediction of the dynamic properties of the masonry walls mainly under both in‐plane and out‐of‐plane vibrations.