Peridynamics (PD) is a continuum theory that employs a nonlocal model to describe material properties. The theory assumes that particles in a continuum interact with each other across a finite distance, and formulates problems in terms of integral equations rather than partial differential equations. In this paper, an improved material model for the elastic deformation and quasi-static fracture analysis of materials and structures were proposed within the framework of the PD. The model enables accurately analyzing quasi-static elastic behavior of materials and structures under external loads by implementing a local damping into the peridynamic equations of motion and employing a quasi-static step loading method. The qualitative and quantitative validity of the model was established through numerical examples.