Analytical solutions are developed for the flow and heat transfer in nonisothermal screw extrusion processing of viscoplastic fluids with pressure back flow. The screw geometry is assumed to be shallow and the flight width small, thus enabling the flow to be modeled as that occurring between two infinitely long parallel plates, i.e., the generalized Couette flow. The constitutive equation is the generalized Newtonian fluid and the Herschel-Bulkley viscosity function is used to describe the rheology of the viscoplastic fluid, and the interfacial boundary condition of wall slip is incorporated in the analysis. For the temperature problem, the shear viscosity of the fluid is taken to be independent of temperature, and the equation of conservation of energy is reduced to an eigenvalue problem. The eigenfunctions and eigenvalues are determined using the Runge-Kutta method. The analytical solutions in terms of pressure gradient, and temperature distributions show good agreement with numerical and experimental results in the literature for power law fluids. The analytical results are also compared with experimental data collected from twin screw extrusion processing of a concentrated suspension which exhibits viscoplasticity, and wall slip, with the mass flow rate sufficiently low for the pressure back flow to be significant.