Irreversible changes of the remanent magnetization of fine grains of ferromagnetics under uniaxial compression have been experimentally examined in a systematic way. The compression of a sample in a magnetic field results in a remanent magnetization which is greater than that obtained without compression in the same field. The pressure remanent magnetization PRM produced by removing uniaxial compression in a magnetic field increases with increasing compressional stress. The dependence of the PRM of a fine grain assemblage of titanomagnetite upon pressure P and a magnetic field Hex can be expressed by af(p)Hex, where f(p) increases monotonically with respect to pressure, reaching some limitting value at pressures higher than 2 kb, and a is a numerical constant systematically dependent on grain size. The ratio of PRM/IRM in a weak magnetic field for homogeneous bulk specimens with grain size larger than about 0.1 mm varies from 1 to 5, whereas specimens containing fine grains with diameters less than 0.1 microns have ratios of 20 to 40. A similar grain size dependence is found for Cu-Co superprecipitates containing homogeneously dispersed ferromagnetic fine grains in a non-ferromagnetic matrix. Stability of the PRM of a fine grain assembalge of titanomagnetite has been examined through ac field demagnetization. The decay of PRM with respect to increasing peak intensity of an ac field resembles that of IRM rather than that of ARM.The intensity of various types of remanent magnetization, such as TRM, IRM and ARM, decreases irreversibly as the specimen is compressed uniaxially in a non-magnetic space. The observed hyperbolic decay of remanent magnetization with increasing compressional stress can be accounted for by a PRM induced by the demagnetizing field of the specimen itself in a reverse sense to the initial remanent magnetization. It is shown that the PRM vector deviates from the direction of an external magnetic field toward a plane perpendicular to the compressional axis when the magnetic field is not parallel or perpendicular to the axis of compression. The maximum deflection angle is calculated to be 10 degrees and occurs when the angle between the magnetic field and the compressional axis is about 45 degrees.The mechanism of acquisition of PRM is briefly discussed. A more detailed discussion of the problem will be given in a future paper.