Mechanical pressing of soybean is highly desirable as it provides, at low cost, non-contaminated, protein-rich, low-fat soyflour which can be further processed into nutritious edible foods. Unfortunately, mechanical pressing of this low-fat oilseed ($<$20%) yields only 50-70% of the available oil, in contrast to the solvent extraction method which recovers over 98% of the oil. The main focus of the study was to maximize the oil recovery from soybean using mechanical oil expression by applying two pretreatments, enzymatic hydrolysis and extrusion cooking of soybeans, and by varying the pressing conditions including three applied pressures (20, 40 and 60 MPa), three pressing temperatures (22, 60 and 90°C) and two sample sizes (10 and 20 g). To characterize the material properties affecting mechanical oil expression from soybean a mathematical simulation of uniaxial compression was developed which incorporated the time dependent variation of soybean properties. The mathematical simulation was based on Terznaghi's theory of consolidation for soils and was solved using measured values of the coefficients of permeability, volume change and consolidation. A compression-permeability test cell was specifically developed for these measurements. For validation of the model, in addition to extruded soy, sunflower seeds (oil content ca. 45%) were also compressed under the same pressing conditions. Improvements in oil recovery due to enzymatic pretreatment of soybean were small, while the extrusion pretreatment increased the oil recovery from only a trace for raw soybean to 90.6%. Such oil recovery using mechanical pressing of soybean has not been reported in the past. The measured values of oil recovery, coefficients of permeability, volume change and consolidation for soybean and sunflower seeds were found to vary significantly $(P<0.05)$ with time of pressing, applied pressure, pressing temperature and the size of the sample. For extruded soy samples, the developed model predicted the values of oil recovery versus pressing time with an average error of 15%, while for sunflower seed samples the average prediction error was 40%. The high error values were attributed to the presence of hulls in the sunflower seed samples, as well as error during measurement of the coefficient of permeability. The coefficient of consolidation was found to have the greatest influence on oil recovery. The incorporation of time dependent material properties in the developed simulation was demonstrated to give more accurate and consistent prediction in trends of oil recovery as compared to using constant material properties. The correlationship developed between the oilseed material properties and the oil recovery obtained from uniaxially compressed oilseeds would help researchers and designers to better evaluate the mechanical oil expression equipment and systems. To the extent that the developed model adequately predicted oil recoveries from both sunflower and soybean oilseeds, the model is expected to be applicable to other oilseeds as well.