Compact section : In this section, there is no possibility of local flange or web bucking to prevent attainment of the full sections yield strength. In common terms, the beam will not have a local failure (i.e. your web buckles) before the beam has complete failure. Non - Compact section : one or more of the elements in the beam (e.g. in an I-beam which will be detailed below, those elements are the web and the flange) have the possibility of buckling before the beam is able to attain section plasticity. Slender section is almost always avoided. It buckle locally before reaching yield moment. Understand a slender section is even more extreme than a non-compact section