A first principles study has been performed to systematically evaluate the mechanical properties and stabilities of pristine, hydrogenated and fluorinated silicene (H-silicane and F-silicane) under tension. The uniaxial tension along the armchair (AC) and zigzag (ZZ) directions and the equiaxial tensile strain are considered in this work. The calculated results have shown that the deformation, failure behavior and the ideal strength are anisotropic along the three deformed directions. After hydrogenation and fluorination, the ideal strengths in three deformed directions all reduce while the ideal strains increase. Therefore, the hydrogenation and fluorination increase the toughness. The phonon calculations based on the density functional perturbation theory (DFPT) confirm stabilities of the pristine silicene, H- and F-silicane. The Poisson ratios of three materials along the AC and ZZ directions all exhibit monotone decreasing changes with increasing strain, except that the Poisson ratio of pristine silicene in the zigzag direction increases with increasing strain. The tensile strains decrease the buckling height, as expected, but in a complex function. The second- and third-order elastic constants are determined by least-squares polynomial fitting to the first principles calculations. Our results can help to understand the effect of hydrogenation and fluorination of silicene on its mechanical properties and provide some useful data for the experiments.