The work that is being presented demonstrates that there is a critical point at which the engineering stress–strain diagram’s elastic–plastic region transitions to yield and fracture stresses. This transition is demonstrated using thin-walled specimens made using selective laser melting technology from high-strength aluminum alloys (AlSi10Mg) that have undergone preliminary heat treatment. It was discovered that the strain-hardening coefficient, which was determined in the section from yield strength to fracture strength, and the critical point have a highly statistically significant association (0.83 by Spearman and 0.93 by Pearson). It was possible to derive a regression equation that connected the strain-hardening coefficient with the crucial transition point. The type of stress distribution in the elastic–plastic region changes (the Weibull distribution changes to a normal distribution) as the plasticity of the thin-walled samples increases. Additionally, the contribution of the probability density of the stress distribution described by the Cauchy distribution increases in a mode near the point at which the probability density of the fracture increases.