One binary Zn–40Al and four ternary Zn–40Al–(1, 2, 3, 4) Cu alloys were produced by permanent mould casting at different pouring and mould temperatures. Cooling curves were obtained, and the average cooling rate for each alloy ingot was determined. The hardness, tensile strength, percentage elongation and impact energy of the alloys were measured after studying their microstructure by optical and electron microscopy. The effects of cooling rate and copper content on the structure and mechanical properties of the alloys were investigated. The hardness, tensile strength, percentage elongation and impact energy of the alloys were found to increase with increasing cooling rate. These properties, except percentage elongation, also increased with the increasing copper content of the alloys, but the impact energy and tensile strength decreased when the copper content exceeded 1% and 2%, respectively. As a result of a mathematical evaluation of the experimental data, the relationships between mechanical properties, cooling rate and copper content of the alloys were determined and are presented using three-dimensional graphs.