This paper presents a Lagrangian formulation of elastoviscoplasticity, on the basis of the particle finite element method, for progressive failure analysis of sensitive clays. The sensitive clay is represented by an elastoviscoplastic model that is a mixture of the Bingham model, for describing rheological behaviour, and the Tresca model with strain softening for capturing the progressive failure behaviour. The finite element formulation for the incremental elastoviscoplastic analysis is reformulated, through the application of the Hellinger–Reissner variational theorem, as an equivalent optimisation program that can be solved efficiently using modern algorithms such as the interior‐point method. The recast formulation is then incorporated into the framework of the particle finite element method for investigating progressive failure problems related to sensitive clays, such as the collapse of a sensitive clay column and the retrogressive failure of a slope in sensitive clays, where extremely large deformation occurs. Copyright © 2017 John Wiley & Sons, Ltd.