Summary: Surface motion of an isolated sessile bacterial colony is described by a free surface condition known as the kinematic boundary condition. When the colony is attached to a surface which does not allow slip, a difficulty arises in describing the motion of the contact line at the boundary of the colony. Here we present a new theory which allows for a resolution of this difficulty, by allowing for a `radiative' direction-dependent flux of the medium. In effect, this allows slip to occur near the contact line.