Abstract: The axisymmetric problem of an infinite long fiber perfectly bonded to a viscoelastic matrix which contains an annular crack surrounding the fiber is investigated for the case of tension or torsion loading. After obtaining the Laplace transformed solution from the elastic analysis, a Legendre polynomial method is used to invert the Laplace transform numerically. The time dependent stress intensity factors at the crack tips are presented. The results show that when the annular crack is away from the interface, the normalized stress intensity factors at the crack tips decrease with increasing time.