In this paper, we consider the finite type geometric structures of arbitrary order. The aim of this paper is to solve the integrability problem for these structures. This problem is equivalent to the integrability problem for the corresponding G-structures. The latter problem is solved by constructing the structure functions for G-structures of order ≥ 1. These functions coincide with the well-known ones, see [1], for the first order G-structures, although their constructions are different.
We prove that a finite type G-structure is integrable iff the structure functions of the corresponding number of its first prolongations are equal to zero.
Applications of this result to second and third-order ordinary differential equations are noted.