This paper denes a specic viability domain called backstop viability kernel and 4 proposes a new algorithm that approximates such sets in a compact constraint set of d dimensions. 5 The algorithm uses a set approximation technique based on a sample chosen in a regular grid of 6 n d vertices covering the considered constraint set. We show that, in some conditions, the result 7 of the algorithm is the direct approximation of the backstop viability kernel by this approximation 8 technique. This theoretical result is illustrated on examples for which the viability kernel is equal to 9 the backstop viability kernel and can be derived analytically, using two set approximation methods: 10 the nearest neighbour, ensuring a convergence rate in O(n −1), and a recently developed technique, 11 the recursive simplex stars (resistars), ensuring a convergence rate in O(n −2). 12