Kinematic wave theory is used to study the speed of interfacial waves observed in core annular flows of viscous oils with water. The theory; provides a method for measuring the volume fraction of the core. The results obtained by this method are in very good agreement with experimental data. The model also confirms the observation that for oils lighter than water waves move slower than the core in upward flow, faster than the core in downward flow and at the same velocity of the core in horizontal flow. A general correlation for the core fraction in wavy core annular flows at low annulus-to-core viscosity ratio is proposed.