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Recent results are presented from two‐dimensional LASNEX [G. B. Zimmerman and W. L. Kruer, Comments Plasmas Phys. Controlled Thermonucl. Fusion 2, 51 (1975)] calculations of the indirectly driven hohlraum and ignition capsules proposed for the National Ignition Facility (NIF). The calculations concentrate on two capsule designs, the baseline design that has a bromine‐doped plastic ablator, and the beryllium design that has a copper‐doped beryllium ablator. Both capsules have a cryogenic fuel layer. Primary emphasis in these calculations is placed upon robustness studies detailing various sensitivities. Because of computer modeling limitations these studies fall into two categories: those performed with integrated modeling where the capsule, hohlraum, and laser rays all are modeled simultaneously with the laser power levels as the only energy input; and those performed in a capsule‐only mode where an externally imposed radiative flux is applied to the exterior of the capsule, and only the capsule performance is modeled. Integrated modeling calculations address sensitivities to, e.g., the laser pointing; among other things, capsule‐only calculations address yield degradation due to the growth of hydrodynamic instabilities seeded by initial surface roughnesses on the capsules. Limitations of the calculational models and directions for future research are discussed. The results of the robustness studies performed to date enhance the authors’ confidence that the NIF can achieve ignition and produce 10–15 MJ of capsule yield with one or more capsule designs.