Internal tides may be described by a hyperbolic equation which, for the case of constant buoyancy frequency, has constant coefficients. The equation is solved by using the characteristic geometry and characteristic functions to establish a set of linear algebraic equations in the modal amplitudes. The accuracy of the solutions can be assessed using energy considerations. The capability of the solution technique is demonstrated by simulating the barotropic generation of internal waves over linear topography, with emphasis on near-critical topography, when the solution exhibits high shears and discontinuous behavior at the critical slope. The structure of the waves is determined by the ratio, α, of the bottom slope to characteristic slope. The magnitude of the waves may be estimated by considering the ratio of the baroclinic to the topographic length scales which, for linear slopes, is also given by α. For supercritical slopes, the offshore energy flux varies approximately linearly with α, while for subcritical slopes it varies as α5.