While all oil and gas wells operate at pressures and temperatures greater than ambient conditions, wells that are considered high-pressure and high-temperature experience even more challenging operating conditions. These high-pressure, high-temperature (HPHT) wells have pressures greater than 15,000 psi and/or temperatures in excess of 350 degrees F. These harsh operating conditions result in unique design and safety challenges that are not experienced in more conventional wells. Despite these technical difficulties, the significant resource potential of HPHT wells has attracted development for many years and with advancing technology, the number of HPHT wells is increasing. Permanent downhole barriers are one of the most critical design challenging tools used in HPHT wellbores. These barriers must reliably hold high differential pressures for decades without leaks, movement, or other failure modes. Experimental and validation testing is expensive and inherently limited in duration of the tests. As a result, HPHT-specific nonlinear numerical simulation is used to complement the physical tests for better reliability, safety, and reduced development time. The HPHT design verification analysis is used to demonstrate compliance with engineering standards, regulatory requirements, and independent third-party review. This paper presents an analysis procedure for HPHT completion tools through the results from a case study on a permanent bridge plug, a type of downhole pressure isolation tool. The structural integrity is evaluated for multiple loading scenarios per the ASME BPVC Section VIII Division 3 (2017), and the fatigue analysis is conducted based on well-load histograms during the life of the well in accordance with the ASME BPVC Section VIII Division 2 (2017) and API 5791/ASME FFS-1 (2016). This analysis includes nonlinear finite element analysis, temperature and sour environment effects on materials, and the surface finish effects on structural reliability. The simulations are validated through both component-level and assembly-level testing. The successful implementation of the HPHT design verification analysis played a significant role in the successful and timely development of the downhole pressure isolation tool.