In this paper, the modified Young's moduli in both directions are obtained for the two-dimensional single crystal body with a square lattice by using the continuum approach of continuum mechanics and taking into account only the interaction of neighboring atoms. Separately, an expression is obtained taking into account the linear defects such as vacancies. The values of effective Young's moduli compared with the same values for an infinite crystal lattice. Analyses show that the influences of scale effects and vacancies on the Young's moduli are considerable. In addition, it is shown that the effective Young's moduli have three components: the macroscopic value; factors determining the scale effect; factors determining the vacancy. The last component is analogous to the parameter of the damage of the theory of fracture.