The design of the main current systems of an actively shielded and of an iron shielded MRI device for nuclear resonance imaging, is considered. The model for the analysis of the magnetic induction produced by the current system, is based on the combination of a Boundary Element technique and of the integration of two Fredholm integral equations of the first and the second kind. The equivalent current magnetization model is used for the calculation of the magnetization produced by the iron shield. High field uniformity in a spherical region inside the device, and a low stray field in the neighborhood of the device are required. In order to meet the design requirements a multi-objective global minimization problem is solved. The minimization method is based on the combination of the filled function technique and the (1+1) evolution strategy algorithm. The multi-objective problem is treated by means of a penalty method. The actively shielded MRI system results to utilize larger amount of conductor and produce higher magnetic energy than the iron shield device.