The set of the nonlinear Ginzburg-Landau equations is solved for an Al mesoscopic superconducting triangle of finite thickness. We calculate the distributions of the superconducting phase in the triangle and of the magnetic field in and near the triangle. The distribution of the superconducting phase in the triangle is studied as a function of the applied magnetic field. Possible scenarios of penetration of the magnetic field into the triangle are analyzed. We consider two different states: a single vortex state and a state in the form of a symmetric combination of three vortices and an antivortex with vorticity L-a = -2 ("3 - 2" combination). The free energy calculations show that a single vortex penetrates the triangle through a midpoint of one side. The "3 - 2" combination turns out to be thermodynamically preferable when the vortices are close to the center of the triangle. Equilibrium is achieved when a single vortex (or each component of the "3 - 2" combination) is in the center of the triangle. (C) 2001 Elsevier Science. All rights reserved.