In the past decade, greater emphasis has been placed in nuclear reactor design on passive systems for the removal of decay heat. This study focuses on the passive safety feature of decay heat removal in modular high-temperature gas-cooled reactors (HTGRs). The availability of this feature depends largely on reactor dimensions, power, and initial core temperature. It is assumed that the initial temperatures of fuel, graphite matrix, and coolant are the same, and so are represented by the initial core temperature, which is uniformly distributed throughout the core. However, little is known in general about the relationships among the parameters mentioned above or on the ability of the core to passively reject decay heat. To obtain a general understanding of the relationship of those parameters in HTGRs, analyses were performed, estimating the effects of initial core and soil temperatures and of the presence of structural materials on the maximum core temperature, allowable power, and size. Appropriate sizes were evaluated for reactors with given powers having various maximum power densities and operating at different initial core temperatures. Criticality and burnup analyses for the proposed reactors were performed, and it was found that all reactors with 20 wt% of uranium enrichment can be critical for over 16 years of operation.