Current analytical models for multi-fractured horizontal wells (MFHW) generally neglect reservoir heterogeneity, typical seepage characters of unconventional reservoir, partially penetrating fracture and various fracture damage mechanisms. In this thesis, three linear flow models have been developed to facilitate pressure and rate behavior analysis of shale, tight sand and unconventional reservoir with damaged fractures. These models are validated by comparing with KAPPA Ecrin and are more accurate than previous linear flow models in modeling partially penetrating cases. Field data are analyzed and results prove the reliability of these models. The first model is for heterogeneous shale reservoir with multiple gas transport mechanisms. It subdivides the reservoir into seven parts, namely, two upper/lower regions, two outer regions, two inner regions, and hydraulic fracture region. Fracture interference is simulated by locating a no-flow boundary between two adjacent fractures. The locations of these boundaries are determined based on the boundary’s pressure to satisfy the no-flow assumption. Adsorption/desorption, gas slippage and diffusion effects are included for rigorous modeling of flow in shale. Sensitivity analysis results suggest that larger desorption coefficient causes smaller pressure and its derivative as a larger proportion of gas is desorbed in formation and contributes to productivity. The influences of other parameters, such as matrix II permeability, matrix block size, secondary fracture permeability, hydraulic fracture conductivity, and fracture pattern are also discussed. The second model is for heterogeneous tight sand reservoir with threshold pressure gradient (TPG). The linear flow sub-regions are the same as those of the first model. TPG and pressure drop within the horizontal wellbore are included. Simulation results suggest that TPG affects middle-late time behaviors. Greater TPG results in higher pressure drop and accelerates production decline. But this influence is marginal when TPG is small. Effects of other parameters, such as formation permeability, fracture length, conductivity, and wellbore storage are also investigated. The third model is for heterogeneous reservoir with various fracture damage. In this model, the following possible fracture damage situations are discussed: (1) choked fracture damage (2) partially propped fracture, (3) fracturing fluid leak-off damage, (4) dual or multiple damage effects. Simulation results indicate that choked frature damage influences early-mid time performance. Partially propped section within fracture dominates formation linear flow regime. Only severe matrix impairment near fracture face can have noticeable effects on pressure and rate response. A new parameter, skin factor ratio, is applied to describe the relative magnitude of multiple damage mechanisms. Reservoir heterogeneity and fracture damage make the pressure and rate behaviors deviate significantly from undamaged one but one can distinguish major damage mechanisms even in heterogeneous reservoir.