This study investigates the problems of eccentricity and backlash using an analytical spur gear model with 26 degrees of freedom (DOF). Previous studies have only investigated the case of eccentricity with a parallel shift of the axis of rotation of the gear relative to its geometric axis of symmetry. This study presents a novel method for determining the radius of eccentricity and its angular position at any distance from the bearing support, in which the axis of rotation and the geometric axis of symmetry of the gear are non-parallel. The effect of gear motion in the line of action (LOA) and off-line of action (OLOA) directions on backlash is precisely determined, despite the fact that most studies usually ignore gear displacement along the OLOA direction. Numerical simulations are performed to determine the effect of eccentricity on backlash, and their results confirm that the proposed method for determining the radius of eccentricity for any eccentricity type is correct. A gear slice model is used for dynamic analysis. Results show that the type of eccentricity has a significant effect on the gear dynamics and that eccentricity analyses have to include other cases than merely eccentricity with parallel axes of gears.