  Aims. We construct a new analytical model of a solar coronal loop that is
embedded in a gravitationally stratified and magnetically confined atmosphere.
On the basis of this analytical model, we devise a numerical model of solar
coronal loops. We adopt it to perform the numerical simulations of its vertical
kink oscillations excited by an external driver. Methods. Our model of the
solar atmosphere is constructed by adopting a realistic temperature
distribution and specifying the curved magnetic field lines that constitute a
coronal loop. This loop is described by 2D, ideal magnetohydro- dynamic
equations that are numerically solved by the FLASH code. Results. The vertical
kink oscillations are excited by a periodic driver in the vertical component of
velocity, acting at the top of the photosphere. For this forced driver with its
amplitude 3 km/s, the excited oscillations exhibit about 1.2 km/s amplitude in
their velocity and the loop apex oscillates with its amplitude in displacement
of about 100 km. Conclusions. The newly devised analytical model of the coronal
loops is utilized for the numerical simulations of the vertical kink
oscillations, which match well with the recent observations of decay-less kink
oscillations excited in solar loops. The model will have further implications
on the study of waves and plasma dynamics in coronal loops, revealing physics
of energy and mass transport mechanisms in the localized solar atmosphere.
