Mobile boom cranes are used throughout the world to perform important and dangerous manipulation tasks. Given their mobility, these types of cranes can quickly be moved into position. Generally, their base is then fixed and stabilized before they start lifting heavy materials. The usefulness of these cranes can be greatly improved if they can utilize their mobile base during the lifting and transferring phases of operation. This ability greatly expands the workspace by combining base motion with the rotation, lifting, and luffing motions. Of course, the cranes lose some stability margin when a payload is attached. The stability is further degraded when the payload swings. This Master's Thesis presents a stability study of such cranes. As a first step, a static stability analysis of a boom crane is conducted in order to provide basic insights into the effects of the payload weight and crane configuration. Then, a semi-dynamic method is used to take the payload swing into account. As a final step, the results of a dynamic stability analysis obtained by using a multi-body simulation of the boom crane are compared to the outcomes of the previous approaches. This provides conclusions for the practical application of stability analysis. A control method that limits payload swing, and thereby improves stability, is also presented.