We give an algorithm for computing the $V$-saturation of any finitely generated submodule of $V[X_1,... ,X_k]^m (k \in N, m \in N^*)$, where $V$ is a valuation domain. Our algorithm is based on a notion of "echelon form" which ensures its correctness. The proposed algorithm terminates when two (Hilbert) series on the quotient field and the residue field of $V$ coincide. As application, our algorithm computes syzygies over $V[X_1,... ,X_k]$.