In this paper the rolling friction (rolling resistance) model is studied theoretically and experimentally in undergraduate level fundamental general physics courses. Rolling motions of a cylinder along horizontal or inclined planes are studied by simple experiments, measuring deformations of the underlay or of the rolling body. The rolling of a hard cylinder on a soft underlay as well as of a soft cylinder on a hard underlay is studied. The experimental data are treated by the open source software Tracker, appropriate for use at the undergraduate level of physics. Interpretation of results is based on elementary considerations comprehensible to university students—beginners. It appears that the commonly accepted model of rolling resistance based on the idea of a warp (little bulge) on the underlay in front of the rolling body does not correspond with experimental results even for the soft underlay and hard rolling body. The alternative model of the rolling resistance is suggested in agreement with experiment and the corresponding concept of the rolling resistance coefficient is presented. In addition to the obtained results we can conclude that the project can be used as a task for students in practical exercises of fundamental general physics undergraduate courses. Projects of similar type effectively contribute to the development of the physical thinking of students.