This paper presents a method that analyzes long-term position errors in the SDINS(strap-down inertial navigation system) for underwater vehicle applications. Under the assumption that the initial platform misalignment and the inertial sensor biases are the primary sources of the position errors in the SDINS, an analytic solution is derived based on the error propagation model in which these factors serve as the state variables. By using the vertical channel damping loop within the SDINS, the analytic solution is obtained by focusing on the position error in the horizontal plane. The proposed method enables a mathematical analysis of the SDINS position errors with respect to each error state, observing the oscillation terms such as the Schuler/Foucault frequency and the Earth’s rotation. Thus, the proposed solution is expected to be used as a theoretical basis for the development of the underwater vehicles’ navigation system. The effectiveness of the proposed solution is verified by the results of SDINS position error through computer simulations.