Uniaxial compression tests were carried out on four kinds of well-graded rubber concrete with different rubber volume content (0%, 5%, 10%, 20%). The mechanical properties and failure modes were analysed, and the rubber content was determined when the comprehensive performance of rubber concrete was optimal. Then, the uniaxial compression experiments of the optimal dosage group under different strain rates were carried out, and the energy characteristics of rubber concrete under different strain rates were analysed. Results show that the rubber concrete is characterised by ductile failure, rather than brittle failure of ordinary concrete. With the increase in rubber content, the compressive strength decreases significantly, but the deformation ability is enhanced. When the rubber content is 10%, the compressive strength of rubber concrete reaches the standard, and the deformation ability is the best. The typical energy evolution and transformation process of rubber concrete under compression is that the input energy is first converted into elastic energy and stored; then, the conversion rate of dissipated energy begins to increase, resulting in a large number of micro-cracks on the surface of the specimen. Finally, the elastic energy is rapidly released, and the proportion of the conversion rate of dissipative energy is significantly improved, resulting in the overall failure of the specimen. In addition, with the increase of strain rate, the compressive strength and initial elastic modulus of rubber concrete increase significantly, while the peak strain decreases. At the same time, the total input energy, elastic energy and dissipation energy show an upward trend, and the elastic energy increases more obviously.