A computational methodology for dynamic description of rigid multibody systems with translational clearance joints is presented and discussed in this work. Over the past years, extensive work has been done to study the dynamic effect of the revolute joints with clearance in multibody systems, in contrast with the little work devoted to model translational joints with clearance. In a joint with translation clearance, there are many possible ways to set the physical configuration between the slider and guide, namely: (i) no contact between the two elements, (ii) one corner of the slider in contact with the guide surface, (iii) two adjacent slider corners in contact with the guide surface, and (iv) two opposite slider corners in contact with the guide surfaces. The proposed methodology takes into account these four different situations. The conditions for switching from one case to another depend on the system dynamics configuration. The existence of a clearance in a translational joint removes two kinematic constraints from a planar system and introduces two extra degrees of freedom in the system. Thus, a translational clearance joint does not constrain any degree of freedom of the mechanical system but it imposes some restrictions on the slider motion inside the guide limits. When the slider reaches the guide surfaces, an impact occurs and the dynamic response of the joint is modeled by contact-impact forces. These forces are evaluated here with continuous contact force law together with a dissipative friction force model. The contact-impact forces are introduced into the system’s equations of motion as external generalized forces. The proposed methodology is applied to a planar multibody mechanical system with a translational clearance joint in order to demonstrate its features.