An investigation is made of the stability of a graphite layer, several possible types of deformation being considered. In the first (type I) mode of deformation the lengths of all three bonds starting from any atom in the layer are different, while the translational symmetry of the hexagonal configuration within a layer is still maintained. In the second (type II), alternate hexagons remain regular, but the lengths of the bonds joining them differ from the lengths of the bonds in a hexagon. It is found that there are two types within this category, distinguished as IIA and IIB. No account is taken of the interaction between layers. The calculation is based on the Huckel version of the molecular-orbital method for the $\pi$-electrons, with inclusion of an energy term representing the compression of the $\sigma$-bonds. It is shown that for all three types of deformation, with reasonable numerical values for the parameters, the regular configuration usually adopted does indeed correspond to an absolute minimum of the total energy with respect to these modes of deformation.