The hydrophobic mismatch between the lipid bilayer and integral membrane proteins has well-defined effect on mechanosensitive (MS) ion channels. Also, membrane local bending is suggested to modulate MS channel activity. Although a number of studies have already shown the significance of each individual factor, the combined effect of these physical factors on MS channel activity have not been investigated. Here using finite element simulation, we study the combined effect of hydrophobic mismatch and local bending on the archetypal mechanosensitive channel MscL. First we show how the local curvature direction impacts on MS channel modulation. In the case of MscL, we show inward (cytoplasmic) bending can more effectively gate the channel compared to outward bending. Then we indicate that in response to a specific local curvature, MscL inserted in a bilayer with the same hydrophobic length is more expanded in the constriction pore region compared to when there is a protein-lipid hydrophobic mismatch. Interestingly in the presence of a negative mismatch (thicker lipids), MscL constriction pore is more expanded than in the presence of positive mismatch (thinner lipids) in response to an identical membrane curvature. These results were confirmed by a parametric energetic calculation provided for MscL gating. These findings have several biophysical consequences for understanding the function of MS channels in response to two major physical stimuli in mechanobiology, namely hydrophobic mismatch and local membrane curvature.