The investigation of the effects of cracks or similar weaknesses on the load carrying capacity of structural elements such as columns, beams and shells is an important problem in civil, mechanical and aerospace engineering. In this paper, the buckling of slender prismatic circular columns with multiple non-propagating edge cracks is studied by use of the transfer matrix method. The columns are modeled as an assembly of sub-segments connected by massless rotational springs whose flexibilities depend on the local flexibilities introduced by the cracks. This model enables discontinuity in rotations due to bending moments transmitted by the cracked sections. Eigenvalue equations are established in explicit form for classical columns and written for elastically supported columns. Numerical examples show that the buckling loads are affected considerably by the depths, locations and number of cracks, as expected. In case of a single crack, depending on the support conditions of the columns, the buckling loads show sensitivity or insensitivity to the crack location. For a constant crack depth, a crack located in the section of the maximum bending moment causes the largest decrease in the buckling load. In the study, modifications to take into account the intermediate elastic supports are also presented.