The invention consists on a linear switched reluctance electrical machine that may be operated indistinctly as a generator or a motor, with a series of characteristics that allow the optimization of the mass to power ratio, as well as the manufacturing cost. The machine has several air gaps, crossed by a single magnetic flux, in which the magnetic force is obtained. This flux is fed by a set of coils (6) placed in the active parts, these active parts are two yokes (4) and (5) in which the magnetic flux closes, there might be other active parts in the mentioned magnetic circuit through which the magnetic flux does not close. A set of passive elements, normally the translators (1) and (2), produce, while moving relatively to the active part, a variation of the reluctance of the circuit with respect to the position which causes a magnetic force. The most unique characteristic of the present invention is that the magnetic flux only returns through the two outermost active parts (4-5), allowing the desired reduction in mass, weight and cost.