This paper presents three optimal low-order fully integrated geometrically nonlinear solid-shell elements based on the enhanced assumed strain (EAS) method and the assumed natural strain method for different types of structural analyses, e.g. analysis of thin homogeneous isotropic and multilayer anisotropic composite shell-like structures and the analysis of (near) incompressible materials. The proposed solid-shell elements possess eight nodes with only displace-ment degrees of freedom and a few internal EAS parame-ters. Due to the 3D geometric description of the proposed elements, 3D constitutive laws can directly be employed in these formulations. The present formulations are based on the well-known Fraeijs de Veubeke–Hu–Washizu multifield variational principle. In terms of accuracy as well as effi-ciency point of view, the choice of the optimal EAS param-eters plays a very critical role in the EAS method, therefore a systematic numerical study has been carried out to find out the optimal EAS parameters to alleviate different lock-ing phenomena for the proposed solid-shell formulations. To assess the accuracy of the proposed solid-shell elements, a variety of popular numerical benchmark examples related to element convergence, mesh distortions, element aspect ratios and different locking phenomena are investigated and the results are compared with the well-known solid-shell formulations available in the literature. The results of our numerical assessment show that the proposed solid-shell for-mulations provide very accurate results, without showing any numerical problems, for a variety of geometrically linear and nonlinear structural problems.