The ability of the Rasch model to provide item difficulties and achievement test scores which are invariant is studied. Data for the study were obtained from students in grades 3 through 7 who took the Sequential Tests of Educational Progress (STEP III) Reading and Mathematics Concepts tests during a spring norming study. Each test contained 50 items administered in a 40-minute period. These norming data were collected so as to provide both in-level and out-of-level norms, although only a portion of the full set of norming study data was used. All calibrations to the Rasch model were done using the BICAL program. Separate item difficulty and score scale estimates were obtained for each grade level administered a particular level of the tests. Results indicated that achievement scores and item difficulty parameters could be considered as essentially invariant. Ten of 14 out-of-level regressions of item difficulty estimates on in-level estimates were linear, of unit slope, and had zero intercepts. The remaining four regressions had zero intercepts and were linear but did not have slopes of 1.0. (RL)