  In this paper we describe the structure of the tangent cone of a numerical
semigroup ring $A=k[[S]] \subseteq k[[t]]$ with multiplicity $e$ (as a module
over the Noether normalization determined by the fiber cone of the ideal
generated by $t^e$) in terms of some classical invariants of the corresponding
numerical semigroup. Explicit computations are also made by using the GAP
system.
