The dynamic instability of vibrating systems withviscous damping and having one degree of freedom subjectedto parametric excitation under square wave input isstudied using numerical method.The system considered is thus of the general form:..Aq + cq + [K + Qt(t) Jq = 0where Qt(t) is of stepwise form.For parametric inputs which are periodic, the numericalapproach to stability was carried out using the monodromyor transfer matrix approach. from this monodromy approxima-tion method was developed which was formed to give reasonableresults for systems with known stability properties.The stability boundaries for a single degree of freedomsystem under the square wave input have been established.