A new layer by layer/discrete layer model is presented for the linearly elastic and thermoelastic responses of multilayered composite plates. The transverse variation of the displacement field is defined in terms of a one-dimensional finite element representation, using quadratic Lagrangian interpolations. The laminate thickness is subdivided into a series of one-dimensional finite elements (i.e., thickness subdivisions) whose nodes correspond to planes of constant transverse normal coordinates in the undeformed configuration of the laminate. Each of the displacements and loads is expanded in a double Fourier series in the cartesian surface coordinates. Interface and boundary conditions are exactly verified and exploited to reduce the number of independent generalized displacements, before solving the boundary value problem from the standard variational principle for displacements. This leads to a new model, whose size 3N in 3D, is less than the classic layer by layer approach requiring 3(2N + 1), also in 3D. In addition, this model allows satisfying exactly all the interface and boundary conditions. Numerical evaluations and comparisons with exact 3D elasticity solutions confirm the efficacy of the proposed approach. Finally, the proposed modelling has been extended to the thermoelastic response of laminates and the results are compared with the exact 3D solutions. Temperature distributions required for the thermoelastic analysis are determined from the constrained discrete layer approach previously applied to heat conduction.