Hybrid stress finite elements based on the beam-column theory to trace elasto-plastic and fracture behavior are developed for concrete member with strain-softening characteristics, wherein the damages are point-wise evaluated. Also, determination procedure of incremental load-displacement path including the instability phenomena due to the softening, such as snap-through and snap-back, is presented, and their adaptability and availability are discussed. Numerical and parametric test results, for the cantilever beams composed of idealized strain-softening material and the simply supported concrete beams, wherein are employed the tangential stress-strain relation using the concept of fracture energy, are given with the experimental ones, and show that the present approach have the excellent promising potentiality to reveal the localization of fracture zone and the size effect on nominal flexural strength of concrete.