Contact angle hysteresis (CAH) is critical to superhydrophobicity of a surface. This study proposes a free energy thermodynamic analysis (of a 2-D model surface) that significantly simplifies calculations of free energy barrier associated with CAH phenomena. A microtextured surface with pillar structure, typical of one used in experimental studies, is used as an example. We demonstrate that the predicted CAH and equilibrium contact angles are consistent with experimental observations and predictions of Wenzel's and Cassie's equations, respectively. We also establish a criterion for transition between noncomposite and composite wetting states. The results and methodology presented can potentially be used for designing superhydrophobic surfaces.