  In this paper we establish the existence of monads on Cartesian products of
projective spaces. We construct vector bundles associated to monads on
$\mathbb{P}^{a_1}\times\mathbb{P}^{a_1}\times\mathbb{P}^{a_2}\times\mathbb{P}^{a_2}\times\cdots\times\mathbb{P}^{a_n}\times\mathbb{P}^{a_n}$.
Once the monad on $X$ exists the next natural question is if the cohomology
vector bundle associated to these monads are simple or not. We study these
vector bundles associated to monads on $X$ and prove their stability and
simplicity.
