This paper presents SiMR, a simulator of the Rudimentary Machine designed to be used in a first course of computer architecture of Software Engineering and Computer Engineering programmes. The Rudimentary Machine contains all the basic elements in a RISC computer, and SiMR allows editing, assembling and executing programmes for this processor. SiMR is used at the Universitat Oberta de Catalunya as one of the most important resources in the Virtual Computing Architecture and Organisation Laboratory, since students work at home with the simulator and reports containing their work are automatically generated to be evaluated by lecturers. The results obtained from a survey show that most of the students consider SiMR as a highly necessary or even an indispensable resource to learn the basic concepts about computer architecture.