Carbon dioxide’s (CO₂) ability to reach the supercritical phase (7.39 MPa and 304.15 K) with low thermal energy input is an advantageous feature in power generation design, allowing for the use of various heat sources in the cycle. A small-scale supercritical carbon dioxide (sCO₂) power cycle operating on the principle of a closed-loop Brayton cycle is currently under construction at The University of Texas at San Antonio, to design and develop a small-scale indirect-fired sCO₂ Brayton cycle, acquire validation data of the cycle’s performance, and compare the cycle’s performance to other cycles operating in similar conditions. The power cycle consists of four principal components: A reciprocating piston compressor, a heating source, a reciprocating piston expander to produce power, and a heat exchanger to dissipate excess heat. The work explained in the present manuscript describes the theory and analysis conducted to design the piston expander, heating source, and heat exchanger in the cycle. Theoretical calculations indicate that using sCO₂ for the Brayton cycle generates 4.5 kW of power with the inlet pressure and temperature of 17.23 MPa and 358.15 K to the piston expander. Based on the fully isentropic conditions, the thermal efficiency of the system is estimated to be 12.75%.