This work concerns the analysis of egg packages subjected to compression. Experimental investigations were carried out to determine the curves of compression and maximum loads. To compare packages accessible on the market, several different shapes of egg packages were tested after being conditioned in air with a relative humidity of 50%. Several paper structures in stock were compressed. By validating the experiment results, numerical computations based on the finite element method (FEM) were executed. The estimations of a numerical model were performed with the use of the perfect plasticity of paper and with the assumption of large strains and deflections. Our own two structures of egg packaging were taken into account: basic and modified. The material of the packages was composed of 90% recovered paper and 10% coconut fibres. This paper involved the numerical modelling of such complex packaging. Moreover, our research showed that introducing several features into the structures of the packaging can improve the stiffness and raise the maximum load. Thanks to the application of ribs and grooves, the strength ratio and compression stiffness, in comparison to the basic tray, increased by approximately 23.4% and 36%, respectively. Moreover, the obtained indexes of modified trays were higher than the majority of the studied market trays.