Solid‐state refrigeration represents a promising alternative to vapor compression cooling systems. Solid‐state devices based on magnetocaloric, electrocaloric, and elastocaloric effects have demonstrated the ability to achieve high‐efficiency, reliable, and environment‐friendly refrigeration. Cooling devices based on the barocaloric (BC) effect—entropy change due to applied hydrostatic pressure, however, has not yet been realized despite the significant promise shown in material‐level studies. As a step toward demonstrating a practical cooling system, this work presents a thermodynamic and heat transfer model for a BC refrigerator The model simulates transient thermal transport within the solid refrigerant and heat exchange with hot and cold thermal reservoirs during reversed Brayton refrigeration cycle operation. The model is used to evaluate the specific cooling power (SCP) and coefficient of performance (COP) of the device comprising nitrile butadiene rubber (NBR) as a representative BC refrigerant. Experimentally validated BC properties of NBR are used to quantify the contribution of different operating parameters including cycle frequency, applied pressure, operating temperatures, and heat transfer coefficient. The results show that a BC refrigerator operating with a temperature span of 2.4 K and 0.1 GPa applied pressure can achieve an SCP of 0.024 W g−1 at 10 mHz cycle frequency and a COP as high as 5.5 at 1 mHz cycle frequency—exceeding that of conventional vapor compression refrigerators. In addition, to identify key refrigerant properties, the effect of bulk modulus, thermal expansion coefficient, heat capacity, and thermal conductivity on device performance are quantified. The results highlight the trade‐off between different material properties to maximize the BC response, while minimizing mechanical work and improving thermal transport. This work demonstrates the promise of solid‐state cooling devices based on soft BC materials and provides a framework to quantify its performance at the device‐level.