In this paper we outline a front-tracking method for computing the moving contact line.
In particular, we are interested in the motion of two-dimensional drops and bubbles
on a partially wetting surface exposed to shear flows.
Peskin's Immersed Boundary Method is used to model the liquid-gas interface,
similar to the approach used by Unverdi and Traggvason.
The movement near the moving contact line is modelled by a slip condition,
the value of the dynamic contact angle is determined by a linear model,
and the local forces are introduced at the moving contact lines based on a relationship
of moving contact angle and contact line speed.
Numerical examples show that the method can be applied
to the motion of drops and bubbles on a solid surface over a wide range of parameter values.