An observability analysis for the two-position alignment of strapdown inertial navigation system (SDINS) is performed using an analytic approach utilizing the nonsingular condition of the determinant of a simplified stripped observability matrix. It is then confirmed by employing a numerical calculation of the error covariance propagation using a twelve-state stationary error model of SDINS including a vertical channel. Based on the results, completely observable conditions and degree of observability are introduced for the two-position alignment.