Understanding the relationship between spindle torque, tool kinematics, and material flow is important for the emerging solid-state additive friction stir deposition (AFSD) process. This study presents the first analytical modeling effort to integrate tool kinematics and material flow for the spindle torque prediction in AFSD. In the proposed model, material flow is first inferred by tool kinematics with consideration of slippage. The derived strain rate is then used to calculate flow stress based on the Johnson-Cook constitutive models for different materials. Spindle torque is estimated by integrating the effects of plastic deformation and sliding friction across tool-deposition surface. Experiments of wall deposition using aluminium 7075 feedstock at different spindle speeds are performed. In addition to aluminium 7075, the experimental data of stainless steel 316 in the literature is also applied for model validation. Experimental validation results show that the proposed analytical model can achieve good performance of spindle torque prediction for different deposition materials in AFSD.