  Nearly all previous discussion on beaming effects in GRBs have assumed a
conical geometry. However, more and more observations on relativistic jets in
radio galaxies, active galactic nuclei, and "microquasars" in the Galaxy have
shown that many of these outflows are not conical, but cylindrical, i.e., they
maintain constant cross sections at large scales. Thus it is necessary to
discuss the possibility that GRBs may be due to highly collimated cylindrical
jets, not conical ones. Here we study the dynamical evolution of cylindrical
jets and discuss their afterglows. Both analytical and numerical results are
presented. It is shown that when the lateral expansion is not taken into
account, a cylindrical jet typically remains to be highly relativistic for \sim
10^8 - 10^9 s. During this relativistic phase, the optical afterglow decays as
\propto t^{-p/2} at first, where p is the index characterizing the power-law
energy distribution of electrons. Then the light curve steepens to be \propto
t^{-(p+1)/2} due to cooling of electrons. After entering the non-relativistic
phase (i.e., t > 10^{11} s), the afterglow is \propto t^{-(5p-4)/6}. But if the
cylindrical jet expands laterally at co-moving sound speed, then the decay
becomes \propto t^{-p} and \propto t^{-(15p-21)/10} - t^{-(15p-20)/10} in the
ultra-relativistic and non-relativistic phase respectively. Note that in both
cases, the light curve turns flatter after the relativistic-Newtonian
transition point, which differs markedly from the behaviour of a conical jet.
It is suggested that some GRBs with afterglows decaying as t^{-1.1} - t^{-1.3}
may be due to cylindrical jets, not necessarily isotropic fireballs.
