Summary: Existence of multiple positive solutions for a coupled system of nonlinear two-point singular boundary value problems \[ \begin{aligned} -x''(t) &= p(t) f(t,y(t), x'(t)),\quad t\in (0,1),\\ -y''(t) &= q(t) g(t, x(t), y'(t)),\quad t\in (0,1),\\ x(0) &= y(0)= x'(1)= y'(1)= 0,\end{aligned} \] is established. The nonlinearities \(f,g: [0,1]\times[0,\infty)\times (0,\infty)\to [0,\infty)\) are allowed to be singular at \(x'=0\) and \(y'=0\) and the functions \(p,q\in C(0,1)\) are positive on \((0,1)\). An example is also included to show the applicability of our result.