© 2019, Society of Petroleum Engineers.The present work focuses on the stability of drill strings in vertical wellbores. The first rigorous treatment of stability of drill strings for vertical wellbores was presented by Lubinski (1950) and his equation is till most widely used in the industry. Cunha (2004) stated that since Lubinski (1950) used power series to solve differential equation governing the stability problem, and the terms of power series become very large for long drill strings, therefore, after a certain length, the calculations may lead to inaccurate results. Mitchell and Miska (2011) stated that analytical solution for infinite-length drill string is used for deep vertical wells in the industry. The subject studied in this study is of great importance in designing the bottom hole assemblies in deep and ultra-deep vertical wells to eliminate problems associated with instability of drill strings. The study includes Finite Element Method (FEM) solution of critical sinusoidal buckling force for 5 different drill collars with 21 different lengths starting from 1000 ft. up to 25000 ft. The main objectives of the study are to see the difference between post-buckling behavior of slender-dominated long hanging drill strings with stiffness-dominated short hanging drill strings in vertical wellbores; to investigate the effect of flexural rigidity of drill collars on decrease of the critical buckling forces as a length parameter of the drill string; and to see the behavior and amount of decrease in the critical buckling forces as the length of the drill string increases. And, it is showed that critical buckling force decreases as the depth of the well increases according to FEM solutions, although, analytical solution gives only a fixed critical buckling force for a specific pipe independent from the length. Also, it is showed that post-buckling behavior of slender-dominated long hanging drill strings with stiffness-dominated short hanging drill strings in vertical wellbores are different.