This paper presented an analytical method for determining the response of a rigid strip foundation resting on the surface of a viscoelastic half‐space to horizontal dynamic loads, and the associated transient soil displacements resulting from the vibration of the footing. This mixed boundary value problem was solved by means of Jacobi orthogonal polynomials, a more efficient method compared to transforming the dual integral equations resulting from the boundary conditions to Fredholm integral equations. Displacements and stresses of the soil‐footing system were accordingly obtained by applying the inverse Fourier transform. Finally, we used the proposed solution to investigate the effects of material damping and Poisson's ratio of soil on the dynamic response of the strip footing, and the resulting soil displacements.

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