Dependences of the elastic modulus (B T ), Poisson ratio (μ), thermal expansion coefficient (α p ), and specific heat (c v and c p ) on the size and shape of the simple matter nanocrystal with a free surface have been studied using the model of nanocrystal in the form of a rectangular parallelepiped with a variable surface shape (RP model). Specific calculations have been carried out for bcc iron. It is shown that the elastic modulus decreases with an isomorphic (at a constant nanocrystal shape) decrease in the nanocrystal size (number N of atoms), whereas the functions μ(N), α p (N), c v (N), c p (N), and c p (N)-c v (N) increase along the isotherm. The larger the deviation of the nanocrystal shape is from the most energetically stable form (cube for the RP model), the more noticeably the change in these functions is with a decrease in nanocrystal size along the isotherm. It is shown that the size compression of the lattice parameter for a bcc iron nanocrystal increases with a decrease in the nanocrystal size, with a decrease in temperature, or with an increase in the nanocrystal shape deviation from the most energetically stable form.