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The Short Model Coil (SMC) working group was set in February 2007 within the Next European Dipole (NED) program, in order to develop a short-scale model of a dipole magnet. The SMC group comprises four laboratories: CERN/TE-MSC group (CH), CEA/IRFU (FR), RAL (UK) and LBNL (US). The SMC magnet is designed to reach a peak field of about 13 Tesla (T) on conductor, using a 2500 Powder-In-Tube (PIT) strand. The aim of this magnet device is to study the degradation of the magnetic properties of the cable, by applying different levels of pre-stress. To fully satisfy this purpose, a versatile and easy-to-assemble structure has been realized. The design of the SMC magnet has been developed from an existing dipole magnet, the SD01, designed, built and tested at LBNL with support from CEA. The goal of the magnetic design presented in this paper is to match the high field region with the high stress region, located along the dipole straight section. For this purpose, three-dimensional nonlinear parametric models have been implemented using three codes (CAST3M, ANSYS, and OPERA). This optimization process has been an opportunity to cross-check the codes. The results of this benchmarking are presented here, along with the final design which incorporates the use of end spacers and a surrounding iron structure to deliver a nominal field of 13 T uniformly distributed along the cable straight section.