Floating production, storage and offloading units (FPSO) and floating storage and offloading units (FSO) have been and will be built for small or medium size oil fields. Recently the external turret mooring systems (ETM system) for FPSO/FSO are increasing in number, because of easy installation onboard, redundancy of mooring chain (i. e. safty), easy mooring works at site, and economical cost. But there seems no report on the calculation method of maximum mooring force for ETM systems. It is very important to estimate the maximum mooring force at early stage of the design of the mooring system. However, there is no practical calculation method. This report proposes the calculation program of ship motion round a SPM and mooring forces, considering a low frequency surge motion. This program is evaluated by the model test of a 850, 000 bbl FSO and a new calculation method of maximum mooring force is proposed. This method is based on a statistic analysis of surge motion and offset from the initial moored point, under external forces of waves, current and wind. The predicted maximum surge and offset gives the maximum mooring force.