The anisotropic growth of plant cells depends on cell walls having anisotropic mechanical properties, which are hypothesized to arise from aligned cellulose microfibrils. To test this hypothesis and to identify genes involved in controlling plant shape, we isolated mutants in Arabidopsis thaliana in which the degree of anisotropic expansion of the root is reduced. We report here the characterization of mutants at two new loci, RADIALLY SWOLLEN 4 (RSW4) and RSW7. The radial swelling phenotype is temperature sensitive, being moderate (rsw7) or negligible (rsw4) at the permissive temperature, 19°C, and pronounced at the restrictive temperature, 30°C. After transfer to 30°C, the primary root’s elongation rate decreases and diameter increases, with all tissues swelling radially. Swelling is accompanied by ectopic cell production but swelling is not reduced when the extra cell production is eliminated chemically. A double mutant was generated, whose roots swell constitutively and more than either parent. Based on analytical determination of acid-insoluble glucose, the amount of cellulose was normal in rsw4 and slightly elevated in rsw7. The orientation of cortical microtubules was examined with immunofluorescence in whole mounts and in semi-thin plastic sections, and the orientation of microfibrils was examined with field-emission scanning electron microscopy and quantitative polarized-light microscopy. In the swollen regions of both mutants, cortical microtubules and cellulose microfibrils are neither depleted nor disoriented. Thus, oriented microtubules and microfibrils themselves are insufficient to limit radial expansion; to build a wall with high mechanical anisotropy, additional factors are required, supplied in part by RSW4 and RSW7.