Erythrocytes swell owing to the osmotic shock caused by hypotonic liquids, and when the membrane tension exceeds a certain limit, hemolysis occurs. The base tension in the membrane of a spherically shaped erythrocyte is usually ignored in the mechanical evaluation of hemolysis. However, the base tension cannot be ignored when the rigidity of the erythrocyte membrane increases owing to lesions, oxidative stress, and other phenomena. Therefore, it is necessary to re-evaluate the tension level at which hemolysis occurs by considering the increased base tension, which is caused by a combined increase in the bending and shear rigidity of the membrane. To achieve this, we calculated the effect of increases in the combined rigidity on the increases in the internal pressure and membrane tension of the erythrocyte. In this study, assuming the surface area to be constant, the swelling process of erythrocytes was evaluated under the condition that hemolysis does not occur. Evaluation was performed by minimizing strain energy, which is the sum of bending strain and shear strain. When the erythrocyte was spherical, the membrane base tension increased linearly with combined rigidity. Even when the bending rigidity was increased to 100 times that of normal erythrocytes, the effect of the base tension on the hemolysis tension level (15 mN/m) was negligible. However, when shear rigidity was increased to 50-100 times that of normal erythrocytes, it became necessary to decrease the hemolysis tension level by 10% and 20%, respectively, because the base tensions were approximately 1.5 and 3.0 mN/m, respectively.