This study presents an analytical method for the solution of dynamic frictional contact problem between a rigid punch and an isotropic elastic solid. Rigid flat punch moves over the isotropic elastic solid at a constant subsonic speed and friction force develops based on Dahl's friction law instead of Coulomb's dry friction law. Dahl's dynamic friction model is adopted since this model is one of the well-known dynamic friction models in the literature. According to this model, friction force depends only on a displacement rather than the speed of the punch since viscous effects are ignored. Influences of the parameters describing Dahl's friction model on contact stress at slow and high speed sliding cases are examined. Analytical solution is conducted by means of Galilean and Fourier transformations. Friction force is computed numerically by the use of 4th order Runge-Kutta method for various displacements of the punch. Formulation for the contact problem is reduced to a singular integral equation and normal stress over the surface of elastic half-plane is determined. Obtained contact stresses are compared with those generated through finite element method and results display a high degree of accuracy. The influences of direction of motion, Coulomb's coefficient of friction, pre-sliding displacement, asperity stiffness and shape factor of hysteresis loop upon contact stresses and stress intensity factors are revealed.