Numerical studies of wave propagation in free anisotropic plates were conducted at Stanford University in the early 70’s [1,2], followed by a flurry of related work. Yet, this subject has not been completely understood. Recent years, however, have seen greatly increased interests in the influence of the anisotropy of composites and textured metal plates on Lamb wave propagation characteristics. This paper presents the basic theory for the propagation of guided elastic waves in orthotropic plates. Included are both numerical results and analytical or semianalytical expressions for the generalized Rayleigh-Lamb dispersion equations. As examples, comparisons are made of the dispersion curves for isotropic, weakly orthotropic, and strongly orthotropic plates with emphasis on the behavior of the zeroth order symmetric, antisymmetric, and horizontally polarized sheer modes.