The Wilson discretization of the dimensionally reduced supersymmetric Yang--Mills theory is constructed. This gives a lattice version of the matrix model of M-theory. An SU(2) model is studied numerically in the quenched approximation for D=4. The system shows canonical scaling in the continuum limit. A clear signal for a prototype of the ``black hole to strings'' phase transition is found. The pseudocritical temperature is determined and the temperature dependence of the total size of the system is measured in both phases. Further applications are outlined.

PACS numbers: 11.15.Ha, 11.25.Sq