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The Casselman–Shalika method is a way to compute explicit formulas for periods of irreducible unramified representations of 
$p$-adic groups that are associated to unique models (i.e., multiplicity-free induced representations). We apply this method to the case of the Shalika model of 
$\text{G}{{\text{L}}_{n}}$, which is known to distinguish lifts from odd orthogonal groups. In the course of our proof, we further develop a variant of the method, that was introduced by Y.Hironaka, and in effect reduce many such problems to straightforward calculations on the group.
