  We construct two classes of magnetohydrostatic (MHS) equilibria for an
axisymmetric vertical flux tube spanning from the photosphere to the lower part
of the transition region within a realistic stratified solar atmosphere subject
to solar gravity. We assume a general quadratic expression of the magnetic flux
function for the gas pressure and poloidal current and solve the Grad-Shafranov
equation analytically. The solution is a combination of a homogeneous and a
particular part where the former is separable by a Coulomb function in $r$ and
exponential in $z$, while the particular part is an open configuration that has
no $z$ dependence. We also present another open field solution by using a
self-similar formulation with two different profile functions and incorporating
stratified solar gravity to maintain the magnetohydrostatic equilibria, which
is a modification of earlier self-similar models with a twist. We study the
admitted parameter space that is consistent with the conditions in the solar
atmosphere and derive magnetic and the thermodynamic structures inside the flux
tube that are reasonably consistent with the photospheric magnetic bright
points (MBPs) for both open and closed field Coulomb function and self-similar
models as estimated from observations and simulations. The obtained open and
closed field flux tube solutions can be used as the background conditions for
the numerical simulations for the study of the wave propagation through the
flux tubes. The solutions can also be used to construct realistic magnetic
canopies.
