Lipid bilayers are active participants in many crucial biological processes. They can be observed in different phases, liquid and solid, respectively. The liquid phase is predominant in biological systems. The solid phase, both crystalline and gel phases, is under investigation due to its resilience to mechanical stress and tight packing of lipids. The mechanical properties of lipids affect their dynamics, therefore influencing the transformation of cell plasma and the endomembrane. Mechanical properties of lipid bilayers are also an important parameter in the design and production of supramolecular lipid-based drug delivery systems. To this end, in this work, we focused on investigating the effect of solid phases of lipid bilayers on their structural parameters and mechanical properties using theoretical molecular dynamics studies on atomistic models of whole vesicles. Those include area per lipid, membrane thickness, density vesicle profiles, bending rigidity coefficient, and area compressibility. Additionally, the bending rigidity coefficient was measured using the flicker noise spectroscopy. The two approaches produced very similar and consistent results. We showed that, contrary to our expectations, bending rigidity coefficients of solid-ordered bilayers for vesicles decreased with an increase in lipid transition temperature. This tendency was reverse in planar systems. Additionally, we have observed an increase of membrane thickness and area compressibility and a decrease of area per lipid. We hope these results will provide valuable mechanical insight for the behavior in solid phases and differences between spherical and planar confirmations.