Some Rare Decays of Particles within R-parity violating Super-symmetric Model This thesis compares experimental studies of two and three body leptonic decays of mesons (B and K) with theoretical predictions of R-parity violating Minimal Supersymmetric Standard Model. Observables like branching fraction, forward backward asymmetry and polarization asymmetry are studied regarding these decays. Forward backward asymmetry is found to be significant in the case of K ± → π ± μ+μ− only and vanishingly small in case of B ± → K ± μ+μ−. Polarization asymmetry has also been studied in this research work. It is found to be significant only for two body leptonic decays and comparable with standard model in case of three body leptonic decay of mesons. An error analysis of the branching fraction and CP-asymmetry has also been made for three body leptonic decay of mesons. Theoretical predictions for both branching fraction and CP-asymmetry agree well with present experimental data.