This study investigates the dynamics of trapped Rossby waves at high latitudes in zonal ocean currents with linear and jet-like shears. As integration domain, we use a modified β plane (with a rigid boundary at the poleward side), where the second derivative of the Coriolis parameter with respect to latitude is taken into account (Δ term). We distinguish between trapped modal Rossby waves and trapped Rossby wave packets. The former exhibit a monochromatic wave structure alongshore but have a modal structure in the direction perpendicular to the boundary. In contrast, trapped wave packets form a local disturbance and consist of a superposition of a range of different Fourier modes rather than a single wave. We study the propagation and the structural change of barotropic quasi-geostrophic Rossby wave packets by means of a Wenzel, Kramers, and Brillouin (WKB) method and consider also the amplitudes and wave numbers of the corresponding trapped modal waves. The amplitude equation is solved either by the WKB method or by analytical and numerical techniques. Basic flows and wave frequencies are prescribed in such a way that no critical lines can occur. We compare analytical, asymptotical, and numerical solutions of trapped modal waves and discuss the influence of the Earth's sphericity on the wave packet propagation and on the eigenvalues and eigenfunctions of the trapped modal waves. Dispersion diagrams of the coastally trapped modal Rossby waves in the considered shear flows are also presented. The dispersion curves show that trapped modal Rossby waves exist for a wide range of different basic flow amplitudes, shear strengths, and frequencies. It further turns out that for a high-latitude β plane, the Δ term should definitely be taken into account. We suggest that such a selective Rossby waveguide may play a role in the dynamics of the Antarctic Circumpolar Current. ¿ 2000 American Geophysical Union