A ray-tracing procedure is derived for the new exponential asymptotically bounded (EAB) velocity model introduced in Part I of this paper. The model inherits the properties of a medium with linear-velocity variation in depth in the shallow zone and of a medium with constant velocity in the deep zone. Two types of rays departing from the source point on the earth's surface exist in this model, depending on the takeoff angles. The rays of the first kind are symmetric arcs that return up to the earth's surface and have a limited maximum depth of propagation. The rays of the second kind propagate down to infinite depth. In the shallow region, they are curved lines, but at large depth they become asymptotically straight. The form of the ray is governed by the takeoff angle at the source point, where a critical angle splits the two kinds of rays. This critical angle depends only on the ratio between the velocity at the source point and the asymptotic velocity of the EAB model. We derive the formulae required to calculate the two kinds of rays and solve the inverse problem of two-point ray tracing. Finally, we construct the 2D- and 3D-isochron surfaces for a finite offset.