Considering the influence of soil thickness, the vertical vibration response of rigid strip footings resting on viscoelastic soil is theoretically investigated. Based on the assumptions for footing and foundation with rigid bedrock boundary condition, employing the method of Fourier transform, this mixed-boundary value problem is expressed as a pair of dual integral equations, which are transformed to a set of linear equations by means of Jacobi orthogonal polynomials and solved numerically. The solution in this study is compared with the solution of elastic half-space in the literature to verify its rationality. The results demonstrate that the attenuation of ground waves generated by the vibration of the footing, as well as the variation in dynamic compliance coefficient of the foundation, is sensitive to the thickness of the foundation soil layer. The numerical results suggest that considering the foundation soil as infinite half-space, as in existing solutions, is reasonable only in cases where the thickness of the top soil layer exceeds approximately 50 times the width of the footing.