Although melting of a solid is one of the most popular phase transformations, no accepted theory for describing the instability of crystals at the onset of melting has been established yet. Besides a simple crystal-to-liquid transformation, a number of phase transformations, such as the solid-state amorphization and the breakdown of superconductivity of Type II superconductors in magnetic fields, can be understood as a sort of melting. Therefore, it is important to understand how crystals start to melt. There has been a lot of attempts to clarify a triggering mechanism for melting of crystals. Among them, the Lindemann melting criterion offers a simple idea that the lattice instability would occur when the amplitude of thermal atomic displacement reaches some critical value. In the present study, we discuss the validity of the Lindemann criterion by investigating a simple model system, in which the atoms are interacting through the Lennard-Jones potential. For both V-T ensemble and P-T ensemble, we calculate the solid (fcc crystal)/liquid phase boundary for the system by using the molecular dynamics simulation. On the other hand, we can also estimate the solid/liquid phase boundary analytically from thermodynamics by supposing the Lindemann criterion as well as the Mie-Grüneisen equation of state. These two results of phase boundary derived from different methods coincide well in a wide temperature range on both V-T and P-T plane, which tells us that the Lindemann melting criterion should hold for this system.