  We have found that the conventional generic dynamical model for gamma-ray
bursts (GRBs) cannot reproduce the Sedov solution in the non-relativistic
limit. Based on our refined generic dynamical model, we investigate afterglows
from jetted GRB remnants numerically. Many new results are reached. For
example, we find no obvious break in the optical light curve during the
relativistic phase itself. But an obvious break does exist at the transition
from the relativistic phase to the non-relativistic phase, which typically
occurs at time 10 to 30 days. It is very interesting that the break is affected
by many parameters, such as the electron energy fraction, $\xi_{\rm e}$, the
magnetic energy fraction, $\xi_{\rm B}^2$, the initial opening angle of the
jet,$\theta_0$, and the medium density, $n$. We also find that afterglows from
jetted GRB remnants are uniformly characterized by a quick decay during the
non-relativistic phase, with power law timing index greater than 2.1 .
Afterglows from GRB 970228, 980326, 980519, 990123, 990510 and 991208 can be
satisfactorily fitted if the corresponding GRB ejecta are highly collimated.
