The objective of this work is to examine (by experiments and associated limit analysis approximations) the evolution of the densification process of porous continua subjected to a unidirectional compression. The problem is treated by the limit analysis approach, which leads to bounds for the loading path. The formulation is based on (and compared with) the various modifications of Gurson's yield function. However, rather than using `effective properties' of the bulk, the spatial distributions (of the density, of the hydrostatic pressure, etc.) are preserved, along with their time-like progression during the considered nonsteady process. An admissible velocity field is assumed for the bulk material and it is used to find the constitutive response of the material to the densification. Concurrently, an admissible yielding stress field is employed for providing a rigorous lower bound analysis and for assessing the effect of hydrostatic stress on the plastic flow used in the upper bound analysis. The combination of the two admissible fields is shown to provide a satisfactory engineering tool, to predict what should be the loading path for performing the densification, regardless of the actual mechanism by which the densification process is evolved. The suggested procedure is compared to experiments with various sintered powder materials.