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We are interested in the efficiency of the so called Haselgrove’s method (cf. [Math. Comp. 15 (76) (1961) 323; Math. Comp. 39 (160) (1982) 549]) for the evaluation of the multiple integral I=∫01∫01⋯∫01f(x1,x2,…,xp) dx1 dx2⋯dxp.This is a kind of Monte Carlo method but different from it in two points:(1)procedure of taking arithmetic mean is improved,(2)employment the Weyl sequences, as random numbers, with a suitable set of irrational numbers.The precision of the usual Monte Carlo method is O(N−1/2), where N denotes the sample size, while it is O(N−r),r≥1 for Haselgrove’s method.The aim of this report is to give some results of numerical experiments and discuss its efficiency. We will also refer to its application to the numerical solution of some partial differential equations. In Section 1, we give a brief sketch of this method. In Section 2, we will explain how we prepared the numerical experiments, show the results and discuss its efficiency. In Section 3, we consider its application to the numerical solution of PDEs and show some experimental results. [Copyright &y& Elsevier]