A simple theoretical model of the imaging mechanism of underwater bottom topography in tidal channels by real and by synthetic aperture radar (SAR) is presented. The imaging is attributed to surface effects induced by current variations over bottom topography. The current modulates the short-scale surface roughness, which in turn gives rise to changes in radar reflectivity. The bottom topography-current interaction is described by the continuity equation, and the current-short surface wave interaction is described by weak hydrodynamic interaction theory in the relaxation time approximation. This theory contains only one free parameter, which is the relaxation time. It is shown that in the case of tidal flow over large-scale bottom topographic features, e.g., over sandbanks, the radar cross-section modulation is proportional to the product of the relaxation time and the gradient of the surface current velocity, which is proportional to the slope of the water depth divided by the square of the depth. To first order, this modulation is independent of wind direction. In the case of SAR imaging, in addition to the above mentioned hydrodynamic modulation, phase modulation or velocty bunching also contributes to the imaging. However, in general, the phase modulation is small in comparison to the hydrodynamic modulation. The theory is confronted with experimental data which show that to first order our theory is capable of explaining basic features of the radar imaging mechanism of underwater bottom topography in tidal channels. In order to explain the large observed modulation of radar reflectivity we are compelled to assume a large relaxation time, which for Seasat SAR Bragg waves (wavelength 34 cm) is of the order of 30--40 s, corresponding to 60--80 wave periods.