Construction materials are being exploited by mankind posing a risk of their sustainability. On the other hand, many industries are producing waste by-products and their safe disposal is a major challenge to engineers and environmentalists. Identifying waste materials that resemble in properties with some ingredient of concrete can solve this problem to some extent. The aim of this study is to determine the feasibility of utilising two industrial by-products as a replacement of both fine aggregate and coarse aggregate. Granite powder and cockle shell are adopted as partial replacements to fine and coarse aggregate respectively. It is concluded from the study that maximum strength is attained with a combination of granite powder and cockle shell at 20% and 15% partial replacements of fine and coarse aggregate respectively for M30 grade Concrete. The compressive strength for 28 days at these combinations is 43.7 MPa which is 43.75% higher than that of conventional concrete.