Abstract. The continued detection of binary systems among pre-main-sequence stars suggests that fragmentation is a very frequent process during the early stages of star formation. However, the fragmentation hypothesis rests only upon the results of three-dimensional hydrodynamics code calculations. The validity of isothermal fragmentation calculations was questioned by the results of Truelove et al. (1997), and more recently, of Boss et al. (2000), who found, working at very high spatial resolution, that a particular Gaussian cloud model collapsed isothermally to form a singular filament rather than a binary or quadruple protostellar system as predicted by previous calculations. Sufficiently high spatial resolution is necessary to resolve the Jeans length and hence avoid artificial fragmentation in isothermal collapse calculations. Here we use an adaptive, spherical-coordinate hydrodynamics code based on the "zooming" coordinates to investigate the isothermal collapse of centrally condensed (Gaussian), prolate (2:1 axial ratio) cloud core models, with thermal energy α ≈ 0.22 and varied rotational energy (0.246 ≤ β ≤ 0.00025), to discern whether they will still undergo fragmentation into a protostellar binary system, as found in most previous prolate cloud collapse calculations, or condense all the way into a thin filament, as suggested by the linear analysis of Inutsuka & Miyama (1992) and the findings of Truelove et al. and Boss et al. for the spherical, Gaussian cloud model. The prolate clouds all collapsed self-similarly to produce an intermediate barlike core, which then shrank indefinetely into a singular filament without fragmenting. Collapse of the bar into a thin filament also occurred self-similarly, with the forming filaments being much longer than the Jeans length. Since the filaments form at maximum densities that are typical of the transition from the isothermal to the nonisothermal phase, gradual heating may retard the collapse and allow fragmentation of the filament into a binary or multiple protostellar core, as required to explain the high frequency of binary stars.