A numerical procedure is described for predicting wave drift forces and low frequency motions in short crested waves. In calculations of drift forces, wave directional spreading is treated exactly but difference of frequencies is approximated by Newman's assumption. Quadratic transfer functions of drift forces due to arbitrary combination of two waves of the same frequency from different directions are derived based on Newman's far field theory, and numerical calculations are carried out by using three dimensional source technique. Two kinds of moored structures (storage oil tanker and semi-submersible platform) are chosen as the numerical calculating models for investigating the influence of wave directional nonlinear interference on slowly varying drift forces. It is shown that nonlinear interference of wave direction on drift forces is dominant for tanker model, and it is relatively weak for semi-submersible platform so that Newman's frequency assumption can be extended to directional spreading. Furthermore, drift forces in mean wave direction are increased with narrow wave directional distribution (approaching long crested waves), and then drift force in other direction and yaw moment are decreased correspondingly. The mean drift forces for a set of parameters of wave directional distribution and the different mean wave periods are compared with results of the model tests. Finally, effect of wave directional distribution and directional nonlinear interference on low frequency motions of moored semi-submersible platform are discussed by time domain simulations. It is revealed that the neglect of wave directional nonlinear interference can be accepted. The numerical simulations are in good agreement with the model tests by Takezawa etal.