We apply the spherical infall model to compare the observed distribution of radial velocities of galaxies around Coma with predictions that are based on optical and X-ray overdensity profiles. Two optically selected galaxy catalogues, the CfA redshift survey and a UKST plate scanned with the APM, are used to determine the overdensity profile of the cluster. The two sets of predicted caustics in the angular separation-redshift diagram are compared with a radial velocity catalogue which we have extended significantly in the range between 10 and 40 from the centre of the Coma cluster. In total, we have measured 98 new redshifts. Despite almost doubling the number of radial velocities in this interval, we fail to find the caustics with any degree of certainty. Using recent X-ray-based density profiles of Coma, we derive an independent prediction of the caustics in redshift space. The velocities predicted using these X-ray profiles are in general agreement with the observed velocity distribution. We also investigate the effect that non-spherical mass distributions have on the velocity field in the halo. For a velocity field that is constant on concentric ellipsoids, we show that the caustics are blurred, providing a natural explanation of why we do not see the caustics in Coma.