Context. Accurate knowledge of the morphology of halos and its evolution are key constraints on the galaxy formation model as well as a determinant parameter of the strong-lensing phenomenon. Large-scale cosmic simulations are a tailored tool used to obtain statistics on the shape and mass distributions of these halos according to redshift. Aims. Using the cosmological hydrodynamic simulation, the Evolution and Assembly of GaLaxies and their Environments (EAGLE), we aim to provide a comprehensive analysis of the evolution of the morphology of galaxy halos and of their mass distributions with a focus on the snapshot at redshift z = 0.5. Methods. We developed an iterative strategy involving a principal component analysis (PCA) to investigate the properties of the EAGLE halos and the differences in alignment between the various components. The semi-axes and orientation of the halos are estimated taking into account sub-halos in the simulation. The mass distributions of the dark-matter (DM), gas, and star halos are characterised by a half-mass radius, a concentration parameter and (projected) axis ratios. Results. We present statistics of the shape parameters of 336 540 halos from the EAGLE RefL0025N0376 simulation and describe their evolution from redshift z = 15 to z = 0. We measured the three-dimensional shape parameters for the DM, the gas, and the star components as well as for all particles. We also measured these parameters for two-dimensional projected distributions. At z = 0.5, the minor axis of gas aligns with the minor axis of DM for massive halos (M > 10¹² M_⊙), but this alignment is poorer for less massive halos. The DM halos axis ratios b/a and c/a have median values of 0.82 ± 0.11 and 0.64 ± 0.12, respectively. The gas in halos that also contain stars has a more flattened shape, with b/a = 0.70 ± 0.19 and c/a = 0.38 ± 0.20. The sphericity of gas in halos w/ and w/o stars appears to be negatively correlated to the total mass, while the sphericity of DM is insensitive to it. The measured projected axis ratios, b_p/a_p, of star halos at z = 0.5 have a median value of 0.80 ± 0.07, which is in good agreement with ground-based and space-based measurements within 1σ. For DM halos, we measure a value of 0.85 ± 0.06. The evolution of the concentration as a function of redshift is fairly homogeneous for the various components, except for the starless gas halos, which appear much more concentrated for z > 0.7.