This paper presents a constitutive model for linear viscoelastic orthotropic solids containing a fixed level of distributed cracks. The model is formulated in a continuum damage mechanics framework using internal variables taken as second rank tensors. Use is made of the correspondence principle for linear viscoelastic solids to define a pseudo strain energy function in the Laplace domain. This function is then expressed as a polynomial in transformed strain and tensorial damage variables using the integrity bases restricted by the initial orthotropic symmetry of the material. The constitutive relationships derived in the Laplace domain are then converted to the time domain by using the inverse Laplace transform. The model is applied to the specific case of cross-ply laminates with transverse matrix cracks. The material coefficient functions appearing in the model are determined by a numerical (finite element) method for one cross-ply laminate configuration at one damage level. Predictions of the viscoelastic response are then made for the same laminate at other damage levels and for other cross-ply laminate configurations at different damage levels. These predictions agree well with independently determined time variations of properties by an analytic method (Kumar and Talreja, 2001, Linear viscoelastic behavior of matrix cracked cross-ply laminates. Mechanics of Materials 33 (3), 139-154) as well as with the numerically calculated values. Extension of the model to incorporate effects of transient temperature, physical aging and moisture is outlined