In this work three dimensional hybrid-Trefftz stress finite elements for plates and shells are proposed. In hybrid-Trefftz elements two independent fields are approximated: stresses within the element and displacement on its boundary. The required stress field is derived from the Papkovitch-Neuber solution of the Naiver equation, which, a priori satisfies the Trefftz constraint. The required stress field is generated by a new homogeneous harmonic polynomials interpolation base. A restriction to the maximum degree of the monomials of z is imposed, therefore restricting the number independent terms available. Explicit expressions of the corresponding independent polynomials are listed up to the twelfth order. In this work, illustrative applications to evaluate displacements and stresses are carried out by hexahedral hybrid-Trefftz stress element model. The hierarchical p-refinement and h-refinement strategy are exploited in the numerical tests.