Economic production from unconventional gas reservoirs require horizontal drilling with multistage fracturing. These unconventional gas reservoirs include shale, tight gas reservoirs. Since there has been a lot of interest in exploration and production of these systems in past few years, it is very important to understand the pressure response of these systems. This thesis presents forward and backward solutions for the pressure transient analysis of composite dual porosity systems. The forward solution consists of a generalized numerical model that predicts the wellbore pressure response by taking reservoir properties as inputs. Although the presented numerical model has been validated to provide forward solutions for gas reservoirs with vertical and horizontal wells, this study only focuses on gas reservoirs with horizontal wells. Backward solution is used to calculate reservoir properties from the field data. In this study, type curves have been presented for composite dual porosity systems with horizontal gas wells to provide the backward solution. The presented type curves have been shown to predict correct reservoir properties if one has field wellbore pressure response.