The induced magnetization of an isotropic type-II superconductor with an anisotropic sample shape has been measured in an oblique magnetic field and separated into its reversible and irreversible contributions. The measurements unexpectedly show that the irreversible magnetization is oriented essentially parallel to the smallest sample dimension, and is almost independent of the angle of the applied field. This behavior can be understood by considering the critical-state model when the applied field is at an arbitrary direction with respect to the sample axes.PACS numbers: 74.60.Ge, 74.30.CiMuch recent work has focused on the anomalous effects of a magnetic field applied at an angle to the a-b planes of the anisotropic high-7V copper oxide superconductors [1-7]. Observed anisotropy in the irreversible (pinned) behavior is interpreted as being due to the intrinsic anisotropy of the material [1-5]. We have found, however, that when vortex pinning is present, even isotropic type-II superconductors exhibit unexpected results which can be explained as being due purely to sample shape considerations. For bulk parallelepipeds with geometrical aspect ratios as low as 2:1, the irreversible magnetization is oriented essentially parallel to the smallest dimension and does not change as the angle of the applied field is varied from perpendicular to greater than a 45° angle. This unexpected observation is shown here to result from the Bean critical-state model [8] modified to include an applied field at an angle with respect to the sample axes.The measurements were made on polycrystalline Nb and Pb-Bi alloys. The applied field H a was cycled between H C 2 and -H C 2. The induced magnetization density M, due to the macroscopic screening currents, was measured using a vibrating sample magnetometer to determine the component of M along H a , A/VSM, and a torque magnetometer to determine the component of M perpendicular to H a , M {or . All measurements were made at 4.2 K.There are two contributions to M: (a) a reversible part M r due to a screening current near the sample surface and associated with the expulsion of the magnetic field, and (b) an irreversible part M, associated with pinning of the vortices and the resultant vortex density gradient and screening current throughout the sample. The reversible contribution below H c \ equals -H/4K (the usual Meissner effect) and above H c \ is determined by the repulsive interactions of the vortices [9,10]. Demagnetization corrections due to geometry increase the absolute value of the initial slope above 1/4/r and cause M r to lie along a direction different from H a [9-11]. The irreversible contribution results from pinning of the vortices as they attempt to enter or leave the sample (in increasing or decreasing applied fields, respectively). A critical state is set up in which a vortex density gradient and a concomitant critical current J c flows throughout the sample, resulting in a magnetization A// [8,12]. The sign of the gradient, the direction of the current flow, and hence t...