The existence of weak solutions to the quasistatic problems in the theory of perfectly elasto-plastic plates is studied in the framework of the variational theory for rateindependent processes. Approximate solutions are constructed by means of incremental variational problems in spaces of functions with bounded hessian. The constructed weak solution is shown to be absolutely continuous in time. A strong formulation of the flow rule is obtained.(2) constitutive equation:where ν(x) is the outer unit normal to ∂Ω and C is the rigidity tensor. The symbol N K (ξ) denotes the normal cone to the set K at the point ξ in the sense of convex analysis. The problem is supplemented by initial conditions at time t = 0.The boundary conditions u = 0 and ∂u ∂ν = 0 on ∂Ω reflect the mechanical assumption that the plate is clamped.The existence of weak solutions for variational problems in the theory of perfect plasticity was extensively studied during last decades (see, for example, Refs. 1, 2, 5, 6, 10, 14, 16 and 17). In this paper we develop an energy approach to the existence of weak solutions of this problem (Definition 4.1 below), which turns out to be particularly useful for studying their further differential properties (see Ref. 8). The particular case of perfectly elasto-plastic plates has been studied by many authors, subject to various boundary conditions (see, for example, Refs. 3, 7 and 17). We examine here the quasi-static analogue of static problem, studied in Refs. 7, 15 and 17.The aim of this paper is to develop a new approach to the existence of weak solution to problem (1)-(5) (see Definition 4.1 below) in the spirit of the energy formulation of rate-independent problems, studied in Ref. 13. The advantage of this general approach is twofold. On the one hand, it allows to obtain a weak formulation of the flow rule (5) in a measure-theoretic sense, on the other hand, it is crucial in the proof of further differentiability properties of M (t, x), that will be obtained in Ref. 9. As is usual in the energy approach (see Refs. 4, 5 and 13), we obtain the existence of solutions by a time-discretization procedure: first, we consider a sequence of incremental minimum problems and show that an appropriately constructed sequence of piecewise-constant approximations has a bounded variation and satisfies the so-called discrete energy inequality. Then, by using a version of Helly theorem, we extract a converging subsequence, whose limit satisfies (2)-(4), a relaxed form of (1) and an energy equality. These conditions are considered a weak formulation of the original problem.By construction this weak solution has bounded variation with respect to time. The energy equality allows one to prove that it is actually absolutely continuous.At the end of the paper we follow the arguments of Ref. 5 to investigate some fine pointwise properties of the tensor of moments M and we prove a weak formulation of the flow rule (5).This paper is the first step of a program of proving higher differentiability of the tensor of moments M . In fa...