Brick and concrete are the main materials contributing to demolition and construction waste. Considering this precedent, the effects of using both residuals in medium strength concretes are analyzed. Waste brick powder is used as a cement replacement in three different levels: 5%, 10%, and 15%, and it is tested in concretes with no recycled aggregates and concretes with 30% of recycled coarse aggregates replacing natural ones. The compressive strength, the flexural strength, and modulus of elasticity are calculated and compared to a control concrete with no brick powder and no recycled aggregates. The effects of the simultaneous use of both residuals on the physical properties of the recycled concrete are highlighted. Results show that 15% of cement can be replaced by waste brick powder together with 30% of recycled aggregates without suffering significant losses in the strength of the final material when compared to a control concrete.