In everyday life, in engineering technology and processes, as well as in mechanical engineering, oblique collisions of bodies are widespread. These collisions can often be analysed numerically using computer programs.However, in many cases involving oblique collision analysis, optimization, and synthesis, it is desirable to derive analytical relationships in a general form. Such analysis can help predict desirable outcomes (e.g. rapid rebound) or prevent undesirable ones (e.g. jamming). This study focuses on deriving analytical relationships using classical mechanics theorems (such as changes in linear and angular momentum) and fundamental principles of physics (including sliding and rolling friction). First, the basic problem of a plane oblique collision between a wheel (or disk-shaped object) and a stationary plane is examined. The derived relationships align with well-established results in shock theory. The second part of the study extends to oblique collisions involving segment-shaped bodies. Analytical equations are derived for specific collision scenarios, which can be applied in further dynamic studies. The third part of the work examines the jumping and collision motion of a segment-type object along an inclined slope. Finally, the study includes computer modelling examples of oblique collisions, performed using the Working Model program, which validate the theoretical findings and demonstrate their practical applicability.