The conventional (direct) interval linear equation problem involves the calculation of an interval solution vector, x_I , of the interval linear system, A_I x_I = b_I , where A_I is an interval matrix and b_I is an interval vector. In this paper, the authors consider the inverse problem: given a matrix A_c , a vector b_c , and an interval solution vector x_I , find the maximum allowable perturbations δ A and δ b such that the solution to the perturbed linear system ( A_c + δ A ) x = ( b_c + δ b ) is contained in the interval solution vector x_I . Separate consideration is given to the cases when only the right-hand vector b_c is perturbed and when only the coefficient matrix A_c is perturbed. Provided that the perturbations are assumed to be restricted, solutions to these inverse problems can be derived.