Abstract.The authors consider the cubature formula for the approximate calculation of triple integrals of highly oscillatory functions by using Lagrange’s polynomial interlineation of functions with the optimal choice of the nodal planes for the approximation of the non-oscillating set. The error of the cubature formula is estimated on the class of differentiable functions defined on a unit cube.

Keywords: integrals of rapidly oscillating functions of many variables, cubature formulas, Lagrange polynomial interlineation and interflation of functions.