We present the results of a comprehensive set of simulations designed to quantify the selection function of the Bright SHARC survey for distant clusters. The statistical signiÐcance of the simulations relied on the creation of many thousands of artiÐcial clusters with redshifts and luminosities in the range 0.25 \ z \ 0.95 and ergs s~1 (0.5È2.0 keV). We created one standard and 19 varied 0.5 \ L X \ 10 ] 1044 distribution functions, each of which assumed a di †erent set of cluster, cosmological and operational parameters. The parameters we varied included the values of b, core radius and ellipticityWe also investigated how nonstandard surface brightness proÐles (i.e., the Navarro, Frenk, & White, or NFW, model) ; cooling Ñows ; and the ROSAT pointing target, inÑuence the selection function in the Bright SHARC survey. For our standard set we adopted the parameters used during the derivation of the Bright SHARC Cluster X-Ray Luminosity Function (CXLF), i.e., and an isothermal ) 0 \ 1, ) " \ 0 b model with b \ 0.67, kpc, and e \ 0.15. We found that certain parameters have a dramatic r c \ 250 e †ect on our ability to detect clusters, e.g., the presence of a NFW proÐle or a strong cooling Ñow proÐle, or the value of and b. Other parameters had very little e †ect, e.g., the type of ROSAT target r c and the cluster ellipticity. At distant redshift (z [ 0.8), elliptical clusters are signiÐcantly easier to detect than spherical ones in the Bright SHARC survey. We show also that all the tested parameters have only a small inÑuence on the computed luminosity of the clusters ("" recovered luminosity ÏÏ in the text) except the presence of a strong cooling Ñow. We conclude that the CXLF presented by Nichol et al. in 1999 is robust (under the assumption of standard parameters), but stress the importance of cluster follow-up, by Chandra and XMM, in order to better constrain the morphology of the distant clusters found in the Bright SHARC and other surveys.