In this paper, a circular three-layer flow model is proposed to study mucus transport in the airways due to air motion caused by mild forced expiration or mild coughing. Mucus is represented by four-parameter viscoelastic fluid, a combination of Maxwell and Voigt elements, whereas air and serous fluid are taken as Newtonian fluids (incompressible). The pressure gradient generated in the fluid layers is assumed to be given by a time-dependent function representing mild forced expiration or mild cough in the airways causing laminar flow. The effect of slip velocity at the mucus–serous interface caused by the presence of surfactant and at the top surface caused by immotile cilia are also taken into account. The roles of rheological properties of mucus on its transport are studied. The effect of serous fluid and its viscosity on mucus transport is also considered.