This paper is concerned with the numerical analyses of finite element methods for the nonlinear backward stochastic Stokes equations (BSSEs) where the forcing term is coupled with $z.$ Under several developed analysis techniques, the error estimates of the proposed semi-discrete and fully discrete schemes, as well as their boundedness, are rigorously presented and established. Optimal convergence rates of the fully discrete scheme are obtained not only for the velocity $u$ and auxiliary stochastic process $z$ but also for the pressure $p.$ For the efficiency of solving BSSEs, the proposed numerical scheme is parallelly designed in stochastic space. Numerical results are finally provided and tested in parallel to validate the theoretical results.