Liquid crystalline elastomers (LCEs) exhibit a unique coupling between polymer network elasticity and liquid crystal orientational order, leading to complex anisotropic and nonlinear mechanical responses. In this work, a continuum-based constitutive framework is developed for LCEs by extending classical nematic rubber elasticity to incorporate director microstretch, non-affine chain deformation, and finite extensibility effects within a thermodynamically consistent formulation. The model is constructed by generalizing the statistical mechanical description of a freely jointed chain to account for director-dependent effects in the chain configuration, resulting in a modified probability distribution. Model predictions are validated against experimental data for uniaxial stretching from independent studies by Zhou et al. and Higaki et al. The framework successfully reproduces stress-stretch responses for multiple initial director angles and accurately captures the experimentally observed rotation of the director toward the stretching axis. The proposed model formulation provides a physically consistent bridge between microscopic chain statistics and macroscopic continuum mechanics, offering a flexible framework for modeling complex deformation mechanics in LCEs.