We have developed a new method to process and interpret sonic waveforms acquired in high-angle (HA) and horizontal (HZ) wells in the vicinity of layer boundaries. Numerical simulations are examined for HA/HZ fluid-filled borehole models, in which sonic tools with monopole and dipole sources operate across a horizontal bed boundary in hard and soft formations. Simulations are performed with a 3D time-domain finite-difference method assuming a sonic logging tool, in which each receiver station consists of eight azimuthal receivers. Instead of conventional processing for monopole and dipole waveforms, which takes the average and difference, respectively, of waveforms acquired with azimuthal receivers, we analyze the waveforms acquired individually by each azimuthal receiver. For dipole sources, we refer to the dispersive signals recorded by individual receivers as pseudo-flexural waves, and we first process them with a weighted spectral semblance method to obtain the frequency dispersion curves. We then apply a correction to the dispersion curves of receivers with specific azimuths to estimate the formation shear slowness. Close to a horizontal bed boundary, we select two azimuths: One of them is the azimuth with the corresponding receiver positioned within the top layer and having minimal sensitivity to the bottom formation. The second azimuth is such that the corresponding receiver is positioned within the bottom formation and has minimal sensitivity to the top formation. Simulations show that the presence of a bed boundary significantly alters the propagation of P-, S-, and flexural waves. Rather than by borehole guided waves, in HA wells, receiver signals generated with a monopole source are mostly influenced by converted P-P and S-S waves induced by the bed boundary. Apparent slownesses of these converted waves are determined by their direction of propagation and the corresponding true formation slowness. Also, values of apparent slownesses are consistently lower than the true formation slownesses. In soft formations, borehole guided pseudo-flexural waves generated by a vertical dipole source show good azimuthal resolution for the HA and HZ wells. Processing the pseudo-flexural waveforms separately for the top and bottom receivers yields unbiased shear slownesses for formations above and below the well, respectively. This procedure enables the accurate evaluation of formation heterogeneity due to the bed-boundary effects.