The work in this paper is concentrated on reflection/refraction phenomena of plane qP/qSV wave through a self-reinforced elastic layer sandwiched between two monoclinic half-spaces. A theoretical approach is given to compute the analytical expressions for reflection and transmission coefficients showing their dependence on relevant parameters. Numerical simulation are performed for a fiber – epoxy resin composites self-reinforced layer sandwiched between Lithium niobate like monoclinic upper and lower strata. Using numerical simulation, dependence of reflection/transmission angles, reflected/transmitted velocities and reflection/transmission coefficient are studies against variation in angle of incidence, normalized wave number and the self-reinforcement parameters for both incident qP and qSV waves. It is found that the resultant deflection angles, velocity and reflection/transmission coefficients are significantly dependent upon elastic coefficients of the media as well as on the self-reinforced parameters. Findings of this paper may help seismologists and geophysicists to enhance knowledge about the rock structures and their elastic properties.