This paper presents the time-domain viscoelastic formulation based on the Carrera unified formulation (CUF) to obtain the response of composite structures submitted to bending loads. The governing equations are obtained through a modified form of the principle of virtual displacement (PVD) for a viscoelastic analysis. The problem is solved using the Laplace transform instead of direct integration to reduce the computational cost. The results demonstrate the strong capability of the time-domain viscoelastic formulation. Overall, the proposed methodology allows the direct implementation of new optimized high order deformation theories including the thickness stretching effect that may be implemented in futures works.