Building on our previous work on passive dynamic walking with quadrupeds, we show that a large variety of gaits can be created completely passively by a quadrupedal model with elastic legs. Similar to the well-known Spring Loaded Inverted Pendulum model for bipeds, we created a conceptual quadrupedal model with elastic massless legs. To obtain a well-defined sequence of ground contact, we defined three distinct phases for each leg: stance, swing, and wait for touch down. Since a leg cannot make contact during swing, modifying the duration of this phase allows us to prevent feet from striking the ground prematurely. Gaits were identified in a single shooting implementation, such that the contact sequence was only influenced by the starting values of the numerical integration. By varying these values, we were able to identify trotting, pacing, walking, toelting, bounding, and galloping within a single model. For each of the identified gaits, we report the footfall pattern, ground contact forces, speed, and first order limit cycle stability.