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Using classic approaches of analytical mechanics, this paper addresses the general problem and provides an analytic and explicit formulation for the stiffness matrix of a generic mooring system layout. This is done around a generic offset position and heading of the floating unit, given the curves of tension vs displacement for each mooring line, for a frictionless seabed. The international benchmark of the Offshore Code Comparison Collaboration Continuation – OC4 is taken as a case study. The use of the analytical formulation is exemplified by systematically varying the mean offset position and heading of the platform, as well as the pretensioning of the mooring system.