  We numerically study an anisotropic shape transformation of membranes under
external forces for two-dimensional triangulated surfaces on the basis of
Finsler geometry. The Finsler metric is defined by using a vector field, which
is the tangential component of a three dimensional unit vector $\sigma$
corresponding to the tilt or some external macromolecules on the surface of
disk topology. The sigma model Hamiltonian is assumed for the tangential
component of $\sigma$ with the interaction coefficient $\lambda$. For large
(small) $\lambda$, the surface becomes oblong (collapsed) at relatively small
bending rigidity. For the intermediate $\lambda$, the surface becomes planar.
Conversely, fixing the surface with the boundary of area $A$ or with the two
point boundaries of distance $L$, we find that the variable $\sigma$ changes
from random to aligned state with increasing of $A$ or $L$ for the intermediate
region of $\lambda$. This implies that an internal phase transition for
$\sigma$ is triggered not only by the thermal fluctuations but also by external
mechanical forces. We also find that the frame (string) tension shows the
expected scaling behavior with respect to $A/N$ ($L/N$) at the intermediate
region of $A$ ($L$) where the $\sigma$ configuration changes between the
disordered and ordered phases. Moreover, we find that the string tension
$\gamma$ at sufficiently large $\lambda$ is considerably smaller than that at
small $\lambda$. This phenomenon resembles the so-called soft-elasticity in the
liquid crystal elastomer, which is deformed by small external tensile forces.
