Summary: We give a direct geometric interpretation of the path model using galleries in the 1-skeleton of the Bruhat-Tits building associated with a semi-simple algebraic group. This interpretation allows us to compute the coefficients of the expansion of the Hall-Littlewood polynomials in the monomial basis. The formula we obtain is a “geometric compression” of the one proved by Schwer, its specialization to the case \(A_{n}\) turns out to be equivalent to Macdonald’s formula.