Abstract Procrustes problem for orthogonal Kronecker products is considered. Given matrices A 2 Rn 2 \Theta k2, T 2 Rn2 \Theta n2; n * k we seek the minimum of the Frobenius norm kT (Q \Omega Q) \Gamma Ak for all orthogonal Stiefel matrices Q 2 Rn\Theta k, QT Q = Ik. We introduce and implement left and right relaxation methods for minimization. Numerical results illustrating performance of both methods are given. 1 Introduction Let A 2 Rm\Theta k and B 2 Rm\Theta p where m * p * k be given matrices. Let kAk = (trace (AT A)) 1 2 denote the standard Frobenius matrix norm. Th