Crumb rubber is basically tiny rubber particles produced from scrap vehicle tires. This rubber is crumbled into uniform tiny particles with the help of shredders. In the present work, an attempt has been made to utilize rubber particles as a partial substitute of fine aggregates in fabricating cement concretes. Concrete is a mixture of cement, coarse aggregates, fine aggregates and water. Rubber particles of size ranging between 0.297 and 0.250 mm are used as a substitute in the proportion of 5, 10 and 15% by weight to partially replace fine aggregates. Grade 43 Portland cement has been used. Mechanical properties such as compressive, flexural and impact strength are experimentally investigated. Further, dynamic characteristics such as damping ratio and natural frequencies of test samples with different amounts of crumb rubber particles are compared with neat cement concrete samples. Experimental data for different mechanical and dynamic properties are obtained by curing test samples in water for a period of 7, 14, 21 and 28 days respectively. Substitution of crumb rubber particles to partially replace fine aggregates results in reasonable improvement in impact resistance. A decrease in compressive and flexural strength is observed. Further, addition of rubber particles improves the damping property of the samples along with a decrease in natural frequencies.