This paper is about the mechanical design of superconducting accelerator magnets. First, we give a brief review of the basic concepts and terms. In the following sections, we describe the particularities of the mechanical design of different types of superconducting accelerator magnets: solenoids, cos-theta, superferric, and toroids. Special attention is given to the pre-stress principle, which aims to avoid the appearance of tensile stresses in the superconducting coils. A case study on a compact superconducting cyclotron summarizes the main steps and the guidelines that should be followed for a proper mechanical design. Finally, we present some remarks on the measurement techniques. ; Comment: Presented at the CERN Accelerator School CAS 2013: Superconductivity for Accelerators, Erice, Italy, 24 April - 4 May 2013