Existence of positive solutions for a coupled system of nonlinear three-point boundary value problems of the type − x ′′ ( t ) = f ( t , x ( t ) , y ( t ) ) , t ∈ ( 0 , 1 ) , − y ′′ ( t ) = g ( t , x ( t ) , y ( t ) ) , t ∈ ( 0 , 1 ) , x ( 0 ) = y ( 0 ) = 0 , x ( 1 ) = α x ( η ) , y ( 1 ) = α y ( η ) , is established. The nonlinearities f , g : ( 0 , 1 ) × ( 0 , ∞ ) × ( 0 , ∞ ) → [ 0 , ∞ ) are continuous and may be singular at t = 0 , t = 1 , x = 0 , and/or y = 0 , while the parameters η , α satisfy η ∈ ( 0 , 1 ) , 0 < α < 1 / η . An example is also included to show the applicability of our result.