The evolution of small, angular dependent velocity disturbances in laminar pipe flow is studied. In particular, streamwise independent perturbations are considered. To fully describe the flow field, two equations are required, one for the radial and the other for the streamwise velocity perturbation. Whereas the former is homogeneous, the latter has the radial velocity component as a forcing term. The normal modes of the system are determined and analytical solutions for eigenfunctions, damping rates and phase velocities are calculated. Then, the initial value problem is treated and the time development of the disturbances is determined.