  Motivated by supersymmetry breaking in matrix model formulations of
superstrings, we present some concrete models, in which the supersymmetry is
preserved for any finite $N$, but gets broken at infinite $N$, where $N$ is the
rank of matrix variables. The models are defined as supersymmetric field
theories coupled to some matrix models, and in the induced action obtained
after integrating out the matrices, supersymmetry is spontaneously broken only
when $N$ is infinity. In our models, the large value of $N$ gives a natural
explanation for the origin of small parameters appearing in the field theories
which trigger the supersymmetry breaking. In particular, in the case of the
O'Raifeartaigh model coupled to a certain supersymmetric matrix model, a
nonsupersymmetric metastable vacuum appears near the origin of the field space,
which is far from the position of the supersymmetric vacuum. We estimate its
lifetime as a function of $N$.
