The construction sector is currently struggling with the reuse of waste originating from the demolition and modernization of buildings and roads. Furthermore, old buildings are gradually being replaced by new structures. This brings a significant increase of concrete debris to waste landfills. To prevent this, many studies on the possibilities of recycling concrete, known as recycled concrete aggregate (RCA), have been done. To broaden the applicability of reused concrete, an understanding of its properties and engineering behavior is required. A difficulty in sustainable, proper management of RCA is the shortage of appropriate test results necessary to assess its utility. For this reason, in the present study, the physical, deformation, and stiffness properties of RCA with gravely grain distribution were analyzed carefully in the geotechnical laboratory. To examine the mentioned properties, an extensive experimental program was planned, which included the following studies: granulometric analysis, Proctor and oedometer tests, as well as resonant column tests. The obtained research results show that RCA has lower values of deformation and stiffness parameters than natural aggregates. However, after applying in oedometer apparatus repetitive cycles of loading/unloading/reloading, some significant improvement in the values of the parameters studied was noticed, most likely due to susceptibility to static compaction. Moreover, some critical reduction in the range of linear response of RCA to dynamic loading was observed.