Elongations of magnetoactive elastomers (MAEs) under ascending–descending uniform magnetic fields were studied experimentally using a laboratory apparatus specifically designed to measure large extensional strains (up to 20%) in compliant MAEs. In the literature, such a phenomenon is usually denoted as giant magnetostriction. The synthesized cylindrical MAE samples were based on polydimethylsiloxane matrices filled with micrometer-sized particles of carbonyl iron. The impact of both the macroscopic shape factor of the samples and their magneto-mechanical characteristics were evaluated. For this purpose, the aspect ratio of the MAE cylindrical samples, the concentration of magnetic particles in MAEs and the effective shear modulus were systematically varied. It was shown that the magnetically induced elongation of MAE cylinders in the maximum magnetic field of about 400 kA/m, applied along the cylinder axis, grew with the increasing aspect ratio. The effect of the sample composition is discussed in terms of magnetic filler rearrangements in magnetic fields and the observed experimental tendencies are rationalized by simple theoretical estimates. The obtained results can be used for the design of new smart materials with magnetic-field-controlled deformation properties, e.g., for soft robotics.