The present paper proposes a new model and method to detect the occurrence of dynamic instabilities and stick-slip in mechanical face seals used in automotive cooling water pumps, in order to improve their performance. A new tribo-dynamic model is presented and used to examine how many and what design parameters influence stick-slip. Mass, moment of inertia, stiffness, damping ratio, friction relationship, viscosity, roughness and wear, compressive strength of different coupling materials, geometrical specifications and temperature are some of the analyzed parameters. Therefore, this work provides a full overview of the influence of design parameters on the stick-slip phenomenon.