The main objectives of this study are (1) to investigate the effects of heating and cooling on the static and dynamic residual properties of 35 MPa (5000 psi) concrete used in the design and construction of nuclear reactor auxiliary buildings in Korea; and (2) to establish the correlation between static and dynamic properties of heat-damaged concrete. For these purposes, concrete specimens (100 mm × 200 mm cylinder) were fabricated in a batch plant at a nuclear power plant (NPP) construction site in Korea. To induce thermal damages, the concrete specimens were heated to target temperatures from 100 °C to 1000 °C with intervals of 100 °C, at a heating rate of 5 °C/min and allowed to reach room temperature by natural cooling. The dynamic properties (dynamic elastic modulus and dynamic Poisson’s ratio) of concrete were evaluated using elastic wave measurements (P-wave velocity measurements according to ASTM C597/C597M-16 and fundamental longitudinal and transverse resonance tests according to ASTM C215-14) before and after the thermal damages. The static properties (compressive strength, static elastic modulus and static Poisson’s ratio) of heat-damaged concrete were measured by the uniaxial compressive testing in accordance with ASTM C39-14 and ASTM C469-14. It was demonstrated that the elastic wave velocities of heat-damaged concrete were proportional to the square root of the reduced dynamic elastic moduli. Furthermore, the relationship between static and dynamic elastic moduli of heat-damaged concrete was established in this study. The results of this study could improve the understanding of the static and dynamic residual mechanical properties of Korea NPP concrete under heating and cooling.