A panel-free method was developed earlier to solve the radiation and the diffraction problems of floating bodies in waves in the time domain. This method has been extended to compute wave interactions with bodies in water of infinite depth and finite depth in the frequency domain. After removing the singularities in the boundary integral equation and representing the body surface exactly by either analytical description or NURBS surfaces, the boundary integral equation can be discretized over the exact body surface by Gaussian quadratures. Accuracy of the method is demonstrated by its application to the radiation and the diffraction problems of a floating hemisphere, a vertically floating axisymmetric cylinder, and a Wigley hull. Computed added-mass, damping coefficients, and wave exciting forces agree well with published results.