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The flow and consolidation of strongly flocculated particulate suspensions in water are common to a range of processing scenarios in the minerals, food, water and wastewater industries. Understanding the compressive strength or resistance to consolidation of these suspensions is relevant to processes such as filtration, centrifugation and gravity settling, where the compressive strength defines an upper boundary for processing. New data for the compressive strength of consolidating flocculated particulate suspensions in water, including alumina and calcium carbonate, are compared with earlier data from the literature and from our own laboratories for several systems, including two earlier sets of data for alumina. The three sets of data for the compressive strength of alumina agree well. Differences are noted for data measured in shear between our own laboratories and others. New data for the shear strength of AKP-30 alumina are also presented, and although the agreement is not as good, the difference is implied to be due to wall slip associated with a difference in measurement techniques. A simple nonlinear poro-elastic model of the compressive strength was applied to the eight sets of compressive strength data and was found to account for most features of the observed behaviour. The agreement strongly supports the mechanistic failure mode in compression for these systems to be one of simple strain hardening. The one feature that it does not account for without invoking a 'ratchet' is the irreversibility of consolidation. It is, however, suspected that wall adhesion might provide such a ratchet in reality, since wall adhesion has been neglected in the analysis of raw compressive strength until recently, notwithstanding the pioneering work of Michaels and Bolger (30). Overall, the data analysis and fitting presented herein indicate a new future for the characterisation of aggregated particulate suspensions in shear and compression whereby a limited data set in both compression and shear, albeit targeted across a wide concentration range, can now be used to predict comprehensive curves for the shear yield stress and compressive yield stress of samples using a simple poro-elastic model. The veracity of the approach is indicated through a knowledge that the behaviour of both parameters is scalar across a wide range of materials and across a wide range of states of aggregation. [ABSTRACT FROM AUTHOR]