  We develop a theory of tunneling spectroscopy in superconducting topological
insulator (STI), i.e. superconducting state of a carrier-doped topological
insulator. Based on the quasi-classical approximation, we obtain an analytical
expression of the energy dispersion of surface Andreev bound states (ABSs) and
a compact formula for tunneling conductance of normal metal/STI junctions. The
obtained compact formula of tunneling conductance makes the analysis of
experimental data easy. As an application of our theory, we study tunneling
conductance in Cu$_x$Bi$_2$Se$_3$. We reveal that our theory reproduces the
previous results by Yamakage {\it et al} [Phys. Rev. B 85, 180509(R) (2012)].
We further study magneto-tunneling spectroscopy in the presence of external
magnetic fields, where the energy of quasiparticles is shifted by the Doppler
effect. By rotating magnetic fields in the basal plane, we can distinguish
between two different topological superconducting states with and without point
nodes, in their magneto-tunneling spectra.
