Porous copper is potentially very attractive for various functional applications such as filters and heat exchanger materials. Within the scope of this study, porous copper samples with dual pore morphologies were fabricated following the space holder technique using a 1:2 mixture ratio of K2CO3 to NaCl as pore formers. The initial compaction pressure required for green body fabrication was systematically varied between 120 and 180 MPa, and the influence of this pressure over porosity, pore morphology, volume shrinkage, and longitudinal elastic constants was systematically studied. Three longitudinal elastic constants of the porous Cu samples were determined following the non-destructive ultrasonic phase spectroscopy method through the measurement of the phase shift vs. frequency spectra along the three orthogonal directions in each sample. When the applied pressure is increased from 120 to 160 MPa and the Cu:PF mixture ratios are 70:30 and 60:40, respectively, the elastic constant values in the green compaction direction (C11) decrease from 34.2 GPa to 7.5 GPa and 23.7 GPa–17.9 GPa. However, for Cu:PF mixture ratios of 70:30 and 60:40, under 180 MPa green compaction pressure C11 increases to 30.9 GPa and 21.2 GPa, respectively. As the applied green compaction pressure increased from 120 to 160 MPa, the samples' average elastic anisotropy ratio initially increased from 0.29 to 0.59 and then decreased to 0.55 at 180 MPa pressure. While the initial increase in anisotropy is due to increased pore flattening with increasing green compaction pressure, the decrease in anisotropy ratio in the samples fabricated under 180 MPa green compaction pressure is due to enhanced sample densification. Contour maps for different properties have been proposed to identify the optimum combination of initial powder composition and green compaction pressure for the intended end application.