  We address the problem of a non-perturbative formulation of superstring
theory by means of the recently proposed matrix models. For the model by
Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT), we perform one-loop calculation
of the interaction between operator-like solutions identified with D-brane
configurations of type IIB superstring (in particular, for parallel moving and
rotated static p-branes). Comparing to the superstring calculations, we show
that the matrix model reproduces the superstring results only at large
distances or small velocities, corresponding to keeping only the lowest mass
closed string modes. We propose a modification of the IKKT matrix model
introducing an integration over an additional Hermitian matrix required to have
positive definite eigenvalues, which is similar to the square root of the
metric in the continuum Schild formulation of IIB superstrings. We show that
for this new matrix action the Nambu-Goto version of the Green-Schwarz action
is reproduced even at quantum level.
