The constants defining a system of linear equations may be subject to incertainties. In this case the induced variations of the solution can be effectively bounded by methods of interval analysis. In the worst case the complexity of this problem is exponential in the number of variables. We consider Rohn's sign-accord algorithm to solve the problem. A parallel version of the method is developed using rounded interval arithmetic. Theoretical considerations as well as numerical tests indicate that the parallelling is efficient (i.e. the speedup is near linear) if an appropriate number of parallel processors is allocated. This number can be estimated before the start of the parallel process.