Monte Carlo simulations have been performed for the linear tangent hard sphere model. The models considered in this work consisted of m = 3 4, 5, 6, and 7 monomer units. For the models m = 3 and m = 4 we find an isotropic fluid and an ordered solid. For the m = 5 model we find the sequence of phases isotropic-nematic-smectic A on compression, and the sequence solid-smectic A-isotropic on expansion. We suggest that the nematic phase for this model is meta stable. For the model in = 6 we observe the phase sequence isotropic-nematic-smectic A on compression, and the sequence ordered solid-smectic A-nematic-isotropic on expansion. We observe a similar sequence on expansion of the m = 7 model. The results for the in = 7 model are in good agreement with those of Williamson and Jackson [J. Chem. Phys. 108, 10294 (1998)]. It was suggested by Flory [Proc. R. Soc. London, Ser. A 234, 73 (1956)] that liquid crystal phases could exist for length to breadth ratios greater than or equal to5.437, i.e., m greater than or equal to6. In this work we place the lower bound at m greater than or equal to5.