This report describes a design analysis of a test article mimicking a core block of a heat-pipe microreactor using the ASME Boiler & Pressure Vessel Code Section III, Division 5, Subsection HB, Subpart B rules. These rules cover the design and construction of elevated temperature nuclear reactor structural components, like the core block of a heat-pipe microreactor emulated by the test article. The purposes of the report are to: (1) provide a step-by-step example of applying the ASME rules to a reasonable core block geometry and corresponding loading conditions, (2) to provide design feedback on the test article, and (3) to evaluate the ASME rules for use in the design of complex heat-pipe microreactor components. The test article design has a relatively short ASME design life, limited by high thermal stresses. The current ASME rules are adequate for evaluating the core block component designs, though they could be optimized to increase the design efficiency and reduce the amount of designer/analyst time required to execute the design process. The report covers both the current, 2019 edition ASME rules and modified, currently unapproved, rules designed to improve the design process for components with complex geometries and high secondary stresses, like the core block test article.