Using a uniaxial localization model, it is shown that parallel elastic restraint increases ductility, while an increase in support flexibility or length of specimen reduces ductility. Statistical macroscopic nonhomogeneity of the specimen is modeled by a system of uniaxial parallel elements of random properties following the normal distribution. The stability analysis and Monte Carlo simulations explain that in such a system an increase of length or support flexibility reduces not only ductility but also the strength of the system. The effect on strength depends on the number of elements (width of specimen), which represents a new non-classical statistical size effect, and on the standard deviation of peak stress values within the parallel system. Existence of an inflection point and the prolonged tail on the descending branch is explained by the nonhomogeneity of the specimen, and the shape of the descending branch, along with the location of the inflection point, is obtained as a function of machine stiffness, parallel elastic restraint, and specimen length and width.