Abstract: A pair of dual integral equations are presented to solve the contact problem of a rigid strip footing on transversely isotropic layered soils. Based on the governing equations of plane strain problem in Cartesian coordinates, the transfer matrix can be obtained through the Fourier transform with respect to the coordinate variable x and the Cayley-Hamilton theorem. Then, the transfer matrix solution of layered soils is obtained in combination with the continuity conditions between two adjacent layers. Considering the mixed boundary conditions of the contact problem, a pair of dual integral equations are derived, which are further converted to linear equations by means of the Jacobi orthogonal polynomials. Finally, the subgrade reactions can be obtained by solving the linear equations. The results of numerical calculation carried out by the corresponding computer program agree fairly well with those by the existing references and FEM software. Further numerical examples are also presented to elucidate the influence of transverse isotropy and stratification of the soils.