An exactly solvable model, which treats the effective barrier potential of the biased metal-insulator-metal tunnel junctions as a trapezoidal potential with an ideal stepped boundary, is presented. Thus, the exact analytic expressions for the electron wave functions and the tunneling probabilities were obtained by solving Schrodinger's equation strictly. It is found that if the longitudinal kinetic energy of the electron, E-x is greater than the shorter side of the trapezoidal potential, in the barrier region Schrodinger's equation has to be solved in the two subregions: where E-x is lower and higher than the barrier height, respectively. In order to compare the ideal stepped boundary model to Brinkman's two approximation models (J. Appl. Phys. 89 (1970) 1915), the graded diffuse boundary and perfectly sharp boundary model, the trapezoidal barrier parameters were determined by fitting the calculated I-V curves to the experimental ones at 77 K. The results show that for three types of junctions (with Au, Ag, and Cu top electrodes), the variations in barrier parameters with the metal electrodes are in agreement with each other.