A spread mooring system (SMS) allows a ship or a floating platform to moor the seafloor using multiple mooring lines at a restricted region with a fixed heading in harsh weather. These systems can be used for the operations of ships of different tonnage at different sea depths. The optimal design of these systems is a challenging engineering problem because of the effects of many design parameters and changing environmental conditions. Modern soft computing techniques allow difficult engineering problems to be solved easily and precisely and are becoming more and more popular. In this paper, Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) as soft computation techniques have been chosen to estimate the hawser tensions and displacements of a spread mooring system. The attained results show both techniques can give consistent indicators for the modelling of dynamic systems. Although these techniques performed very well, the ANFIS model is relatively superior to the ANN technique, considering the accuracy of hawser tensions and displacements in terms of the relative errors and coefficient of correlation obtained for the ANN and ANFIS.