This study presents the applications of plastic limit analysis to offshore foundations and anchors, including the drag embedment anchors (DEAs) for mobile offshore drilling units (MODU’s) and spudcan foundations for jack-up platforms. In deep waters, drag embedment anchors are an attractive option for mooring of semisubmersible platforms due to low installation cost and high holding capacity; on the other hand, jack-up platforms are more stable than semisubmersible platforms but only can be placed in shallow waters. The analyses of anchor capacities are developed for an idealized anchor comprising a rectangular fluke, a cylindrical shank, and a metal chain connected to the shank at the padeye. The anchor trajectory prediction during drag embedment is also developed by considering anchor behavior in conjunction with the mechanics of the anchor line. The results of simulations show that anchors approach at equilibrium condition rapidly during the embedment and both the normalized holding capacity and the anchor line uplift angle remain constants in this stage. Besides the geometry of the fluke, the properties of the shank and soil are also crucial factors in the anchor-soil interaction behavior. Partial failure of mooring systems for floating structures will subject drag anchors to loads having an appreciable component outside of the intended plane of loading. Partial failure of mooring systems during hurricanes in recent years have generated an interest in understanding drag anchor performance under these conditions. The analysis presents the simulations of three dimensional trajectories of an anchor system subjected to an out-of-plane load component. For the conditions simulated in the example analyses, the anchor experienced a modest amount of continued embedment following partial failure of the mooring system; however, the ultimate embedment and capacity of the anchor is much less than what would have developed if the anchor had continued in its original trajectory within the plane of intended loading. The analyses of the spudcan foundation of jack-up units include preloading, bearing capacity, and the displacement assessment. When the contribution of the soil moment resistance is considered, a three-stage assessment procedure is recommended: superposing environmental forces on the plot of yield surface, determining the value of yield function corresponding to the external forces, and computing the factor of safety of the spudcan. The results of the assessment may be ambiguous while the different yield functions are employed to analyze the spudcan in soft clay.