A three-dimensional, time-dependent numerical model is used to simulate the dynamics and thermodynamics of Delaware Bay, River and adjacent continental shelf. This study describes the first attempt to model an estuary and the contiguous shelf as a coupled hydrodynamic and thermodynamic system. Here, in Part 1, a description of the model, boundary conditions and forcing information is provided. Numerical results are compared with surface elevation data at several locations throughout the Bay and the River, as well as with the observations collected by the National Ocean Service during their 1984–1985 circulatory study. It is shown that a vertically-integrated, two-dimensional version of the model predicts realistic amplitudes but with some phase error. The full three-dimensional model reduces the phase error but underpredicts the tidal range; this is due to the higher values of horizontal viscosity required by the three-dimensional model. The model accounts for non-linear, shallow-water effects and reproduces the observed amplification of the high-frequency tidal components from the mouth of the Bay to the head of the River at Trenton.