The problem of an interface crack between a circular fiber and the sur
rounding matrix is considered. The problem is formulated and solved wi
th the help of complex variable methods. It is essential to take into
account the existence of contact zones at the crack tips. The solution
procedure relies on the use of crack opening displacements as the pri
mary variables. Ultimately the governing equations are shown to consis
t of two coupled singular integral equations together with contact and
single valuedness conditions. In general these equations must be solv
ed by numerical methods. Attention is focused on the lengths of the co
ntact zones. It is shown that the lengths of these contact zones are e
ssentially independent of one of the Dundurs parameters.