In the paper, the exact and asymptotic approximate solutions for symmetric and antisymmetric Lamb waves in the homogeneous isotropic elastic film have been analyzed. Using the numerical methods of the theory of continuation of solutions of nonlinear equations, the dispersion curves were calculated for waves with different variability across the layer thickness. Based on the results obtained, the nature of the displacement field and the variability of oscillation forms depending on the wave number were studied. The asymptotic correctness of the Timoshenko and Euler – Bernoulli beam models as long-wave asymptotics of Lamb waves was analyzed.