The inherent flexibility of two-dimensional (2D) materials allows for efficient manipulation of their physical properties through strain application, which is essential for the development of advanced nanoscale devices. This study aimed to understand the impact of mechanical strain on the magnetic properties of two-dimensional (2D) materials using Monte Carlo simulations. The effects of several strain states on the magnetic properties were investigated using the Lennard-Jones potential and bond length-dependent exchange interactions. The key parameters analyzed include the Lindemann coefficient, radial distribution function, and magnetization in relation to temperature and magnetic field. The results indicate that applying biaxial tensile strain generally reduces the critical temperature (Tc). In contrast, the biaxial compressive strain increased Tc within the elastic range, but decreased at higher strain levels. Both compressive and tensile strains significantly influence the ferromagnetic properties and structural ordering, as evidenced by magnetization hysteresis. Notably, pure shear strain did not induce disorder, leaving the magnetization unaffected. In addition, our findings suggest the potential of domain-formation mechanisms. This study provides comprehensive insights into the influence of mechanical strain on the magnetic behavior and structural integrity of 2D materials, offering valuable guidance for future research and advanced material design applications.