Long-lived particles are predicted by numerous theories beyond the Standard Model. This thesis work is dedicated to the study of long-lived neutralinos decaying semileptonically into standard model particles. This decay channel is allowed by R-parity violation in the MSSM framework. A displaced vertex reconstructed with several tracks and an isolated high-$p_T$ muon is the expected typical signature. This search is motivated by the ability of the LHCb detector to reconstruct displaced vertices and by the low $p_T$ threshold of the muon trigger system that allow to study yet unexplored region of the theoretical parameter space. The analysis has been performed for neutralinos masses between $38$ and $198 ~GeV/c^2$ with a lifetime of $5$, $10$ and $50 ~ps$ on data collected from $pp$ collisions at center-of-mass energy of $\sqrt{s} = 7 ~TeV$ and $8 ~TeV$ during 2011 and 2012 at LHCb. The signal determination techniques has been validated with $Z$ and $W$ events with a topology similar to the signal. No evidence of these long-lived states has been observed, and upper limits on production cross-sections have been set.