Results of computer simulation of static mechanical behavior of a body consisting of ∼1000 hard elastic particles have been invoked to discuss some problems of mechanics of disordered (amorphous) and ordered (crystal) bodies: the glass-liquid transition, irreversible deformation (plasticity in a solid and flow in a liquid states), and intermediate (like liquid crystal) state. It has been shown that the existence of two states, solid and liquid; the condition of transition between them; and the fundamental mechanical properties of a solid body, viz., plasticity, strain softening, and localization of deformation within the shear bands, are controlled by the number of physical contacts between the particles, spatial distribution of contacts, and their disintegration under shear deformation. Systems of rigid particles are in a solid or a liquid state depending on the number of interparticle contacts. Solid (glass or crystal) and liquid states were determined from the ability of a system to resist shape change under external force. As a criterion of the liquid-to-glass transition the equality of the number (translational and rotational) of degrees of freedom, ℱ and the number of constraints of these motions, 𝒞, was used (ℱ = 𝒞). A system is solid if ℱ < 𝒞 and is liquid if ℱ > 𝒞. In systems of rigid particles, constraints are due to mechanical contacts (𝒞1) and/or chemical bonds between the particles (𝒞2). Glasses were classified as mechanical (granular systems and metallic glasses) if 𝒞 ≥ 𝒞2, chemical (nonorganic glasses) if 𝒞1≥ 𝒞2, and combined (polymer glasses) if 𝒞1∼ 𝒞2. Some results of computer imitation confirming the transition criterion are presented. Irreversible deformation of the particle assemblies in the liquid state, unlike in the solid one, showed the following features: extremely low yield stress, absence of change in the number of interparticle contacts and the volume of the system during flow, and random distribution of local strains. Shear strain of the liquid assemblies is governed by particle rotation and consists in the changes of particle orientation, while shear strain of a glassy solid is due to the disintegration of interparticle contacts. A relationship between distribution function of particle orientation and shear strain of the body is found. Crystals of rigid elliptic particles are anisotropic and demonstrate solidlike, liquidlike, or intermediate behavior in different directions depending on the arrangement and ellipse eccentricity. Validity of the geometrical concepts for developing the theory of a condensed state is based on the assumption that any interaction potential can be decomposed into two components: hard repulsion and soft attraction, which are responsible for various properties of the materials.