The mechanisms of autowaves propagation through local non-homogeneities in active media relevant to diverse class of physiological systems were studied by means of a computer simulation. The model proposed by Zel'dovich and Frank-Kamenetsky and that of FitzHugh-Nagumo were used for studying autowave tunneling, which in a broad sense implies underbarrier passing. It was shown that for every fixed parameter value corresponding to the degree of non-excitability of local area a critical value for non-excitable zone latitude exists. An autowave overcomes the barrier and continues to propagate when the value of zone latitude is less than critical. Critical conditions for origination of a source of periodical sequence of impulses in excitable medium were found. The source properties, as shown, can be modified by regulation of size of a non-excitable zone and a zone of higher excitability. In particular, the conditions when spatial irregularity behaves as a source of unidirectional and/or asynchronous sequence of impulses were explored.