Stepwise Uncertainty Reduction (SUR) strategies aim at constructing a sequence of sampling points for a function f : Rd → R, in such a way that the residual uncertainty about a quantity of interest becomes small. In the context of Gaussian Process-based approximation of computer experiments, these strategies have been shown to be particularly efficient for the problem of estimating the volume of excursion of a function f above a threshold. However, these strategies remain difficult to use in practice because of their high computational complexity, and they only deliver at each iteration a single point to evaluate. In this paper we introduce parallel sampling criteria, which allow selecting several sampling points simultaneously. Such criteria are of particular interest when the function f is expensive to evaluate and many CPUs are available. We also manage to drastically reduce the computational cost of these strategies using closed form expressions. We illustrate their performances in various numerical experiments, including a nuclear safety test case.