This paper examines the load bearing capacity of medium-length steel cylindrical shells with a circular cutout under the action of axial compression. Numerical simulations were performed for a radius-to-thickness ratio (R/t) ranging from 100 to 500, and an imperfection parameter (alpha) of between 1 and 4. Structural steel and the behavior of perfect plastic material were considered within the scope of the study. The investigation includes the influence of the cutout size and number, radius-to-thickness ratio. The paper also contains a comparison between theoretical predictions, ABAQUS (R) FE results and experimental data for axially compressed cylinders. A reasonable correlation was obtained between numerical predictions and experimental tests. Details relating to the experimental procedure and FE model are provided. A parametric study was conducted to propose empirical equations, estimating the limit load of cylindrical shells as a function of geometry (R/t, alpha and cutout number) and material properties (E, v and sigma(y)). Empirical formulas were produced, fitting a surface plot using the Least Square method, for both the perfect shell structure (reference shell load) and the limit load reduction factor (phi). All variables in the empirical formula were normalized. A stochastic error analysis was used as a tool to measure how the results of proposed equations approach the FE predictions. Finally, based on experimental and numerical results, formulas are presented to calculate the limit load of medium-length shells with and without circular cutouts having a discrepancy not exceeding +/- 10% regarding error analysis.