  Let $G$ be a connected, complex reductive Lie group and $G/H$ a spherical
homogenous space. Let $(X,L)$ be a polarized $G$-variety which is a spherical
embedding of $G/H$. In this paper we classify $G$-equivariant normal $\mathbb
R$-test configurations of $(X,L)$ via combinatory data. In particular we
classify the special ones, and prove a finiteness theorem of central fibres of
$G$-equivariant special $\mathbb R$-test configurations. Also, as an
application we study the semistable degeneration problem of a $\mathbb Q$-Fano
spherical variety.

Differential Geometry;Algebraic Geometry;Representation Theory