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We investigate the leading power corrections to the decay rates anddistributions in the decay $B \rightarrow X_s \ell^+ \ell^- $ in the standardmodel (SM) using heavy quark expansion (HQE) in $(1/m_b)$ and aphenomenological model implementing the Fermi motion effects of the b quarkbound in the B hadron. In the HQE method, we find that including the leadingpower corrections the decay width decreases by about 4% and the branching ratioby about 1.5% from their (respective) parton model values. The dileptoninvariant mass spectrum is found to be stable against power corrections over agood part of this spectrum. However, near the high-mass end-point thisdistribution becomes negative with the current value of the non-perturbativeparameter $\lambda_2$ (the $\lambda_1$-dependent corrections are found to beinoccouos), implying the breakdown of the HQE method in this region. Ourresults are at variance with the existing ones in the literature in both thedecay rate and the invariant dilepton mass distribution calculated in the HQEapproach. As an alternative, we implement the non-perturbative effects in thedecay $B \rightarrow X_s \ell^+ \ell^- $ using a phenomenologically motivatedGaussian Fermi motion model. We find small corrections to the branching ratio,but the non-perturbative effects are perceptible in both the dilepton massdistribution and the Forward-Backward asymmetry in the high dilepton massregion. Using this model for estimating the non-perturbative effects, wepresent the decay rates and distributions for the inclusive process $B\rightarrow X_s \ell^+ \ell^- $ in the SM.Comment: 42 pages, 13 figures (require epsf.sty, rotate); added Eqs. (36),  (37), and (54) to make the paper self-contained. Present manuscript is now  identical to the version accepted for publication in Phys. Rev. D. We  corrected the misprint in eq. 37 (sign of eps-tensor

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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