In this paper, the moving contact problem between the punch and a layer supported by a Winkler type foundation is considered under plane strain conditions. The cylindrical punch moves smoothly with constant velocity over the homogeneous layer. With the use of Galilean transformation and Fourier integral transform, the plane contact problem is converted into a Cauchy type singular integral equation. The singular integral equation is solved numerically by performing the appropriate collocation method, and the contact width, the contact and in-plane stresses are calculated. The results show that the stiffness of the Winkler foundation and the moving velocity have a significant effect on the contact width and the behavior of the stress field.