A modified piezocone penetration test (CPTu) analytical solution based on spherical cavity expansion and critical state soil mechanics (SCE–CSSM) is employed for assessing yield stress, undrained shear strength, and flow parameters in sensitive Leda clay at the Gloucester test site. For sensitive and structured clays, the formulation relies on the mobilized effective stress friction angle ([Formula: see text]) defined at two parts of the stress–strain curve: (i) peak stress ([Formula: see text]) and (ii) maximum obliquity ([Formula: see text]). Input parameters for assessing the overconsolidation ratio ([Formula: see text], where [Formula: see text] is preconsolidation stress and [Formula: see text] is current effective vertical stress) from CPTu results include: undrained rigidity index (IR = G/su, where G is shear modulus and su is undrained shear strength), plastic volumetric strain potential (Λ = 1 – (Cs/Cc), where Cs is swelling index and Cc is virgin compression index), and effective friction angles ([Formula: see text] and [Formula: see text]). A direct CPTu means of assessing the undrained rigidity index in a reliable manner is also developed that gives the Nkt cone factor and matches profiles of undrained shear strength from triaxial compression tests (suTC). The modified solution is also implemented on two additional sites: a sensitive-quick clay in Norway and structured varved clay from New England. Interpretations of the coefficient of consolidation and permeability from pore-water pressure dissipation tests at Gloucester are evaluated using the SCE–CSSM formulation and shown to be comparable with independent laboratory and field tests.