In this paper, we consider the computation in parallel of several entries of the inverseof a large sparse matrix. We assume that the matrix has already been factorized by a direct methodand that the factors are distributed. Entries are efficiently computed by exploiting sparsity of theright-hand sides and the solution vectors in the triangular solution phase. We demonstrate that inthis setting, parallelism and computational efficiency are two contrasting objectives. We develop anefficient approach and show its efficiency on a general purpose parallel multifrontal solver.