This work focuses on the linear two-point boundary value problem y’ = A(x)y + f(x), a < x < b Bay(a) + Bby(b) = y with a view to their solution by some form of parallel algorithm. The theory and practice of current sequential solution methods is reviewed to select a method which exhibits concurrent processing potential. The method selected is a version of multiple shooting. The language Ada is chosen to code the algorithm because of the features available in it, particularly the inbuilt tasking facility for concurrent processing. The efficiency of the parallel code as implemented is demonstrated by a series of numerical experiments, the results of which are summarised m tabular form.