The development of a strapdown inertial navigation system (SINS) for aerodynamically controlled vehicles, which are limited to altitudes below 30 km (that is, a small distance compared with the Earth's radius of about 7000 km), or using the so-called flat-Earth model (FEM), is the principal objective of this work. In dealing with the FEM equations, the north, east, down (NED) frame on the surface of the Earth is taken as an inertial reference frame. Although, this frame is both accelerating and rotating, the accelerations associated with the Earth's rotation are negligible compared with the acceleration that can be produced by a maneuvering aircraft. Also, in this model, the gravity is taken as constant. In developing the SINS for the FEM, the aerodynamic force and moment have dominant roles, depending primarily on such variables as the angle of attack and sideslip, their derivatives, components of the angular velocity of the aircraft, and the control inputs. On the other hand, the SINS deals with such variables as the small-angle rotation vectors. Thus, it was necessary to link both set of variables as state variables of the strapdown FEM as is done in this work. The developed model is relevant for small (less than 200) angles of attack and sideslip.