The article is devoted to a straight rod of variable cross-section. A rod of variable cross-section is loaded with a concentrated force and a distributed load. The boundary between the areas of stability and instability is determined. The study of the stability of deformable systems began a long time ago. Determining the critical loads for compression bars is fraught with significant difficulties. Solving eigenvalue problems is greatly simplified when using numerical methods and modern computer software. A vertically standing column of variable cross-section is considered. The bending of a beam is described by classical theories using Bernoulli’s hypothesis. The curved axis of the beam is described using a linear ordinary differential equation. As a result, a simplified solution to the problem was achieved in non-traditional cases when studies of a rod of variable cross-section and load are combined. Two special examples are considered. The boundaries of the zones of stability and instability are determined. The results presented in the figures have a high degree of accuracy.