In this work we investigate a decidability problem of group version of the knapsack problem for Baumslag-Solitar group BS(p, q). We proved, that the knapsack problem is decidable for group BS(p, q) for coprime integers p > 1, q > 1. In the case when p = 1, q ∈ ℕ, we proved that knapsack problem is decidable for group BS(1, q) with some restriction on the input of the problem. However, the problem of the decidability of the knapsack problem for group BS(1, q) on the whole set of inputs remains open.