The three-dimensional model presented in this paper is used to study how tidal currents form wave-like bottom patterns. Inclusion of vertical flow structure turns out to be necessary to describe the formation, or absence, of all known large-scale regular bottom features. The tide and topography are treated as a coupled system, and the potential free instabilities in this system are investigated. A linear stability analysis is used to study the dynamics of bed forms. This yields information on the role of physical mechanisms; such information cannot be obtained by direct numerical nonlinear simulation. The basic state represents a horizontal elliptical flow, veering in vertical direction, over a flat bottom. It is shown that in such a system, modes can grow which have characteristics of both tidal sand banks and sand waves. The model predictions are compared with observations and show good agreement.