Three-dimensional magnetohydrodynamics of the Solar coronal plasma is investigated by numerical simulation, aiming to understand the mechanisms of the Solar flare onset. It is demonstrated by the simulations that the resistive tearing mode instability growing on the magnetic shear inversion layer can drive the large-scale eruption through the mutual excitation of double reconnections. It is also revealed that the instability is able to cause the magnetohydrodynamic energy relaxation, in which the typical sigmoidal structure is self-organized prior to the onset of eruption. The simulation results predict that both the formation of sigmoids and the onset of flares should occur around the electric current sheet where the magnetic shear is steeply reversed. It is consistent with the reversed-shear flare model and the vector magnetograph observations.