The time-harmonic Lamb problem for a system consisting of an imperfectly bonded covering layer and an orthotropic half-plane is studied. It is assumed that the materials of constituents of the system considered are orthotropic, and the imperfectness of contact conditions is modeled by using a shear-spring model. A plane strain state is considered, and an algorithm for calculating the dynamical stress field is developed and employed. Numerical results on the influence of the shear-spring imperfectness parameter on the distribution of normal contact stresses are presented and discussed. In particular, it is established that the numerical results obtained at limit values of the parameter coincide with the results obtained in the previous work of the authors.