The class of stochastic nonlinear programming (SNLP) problems is important in optimization due to the presence of nonlinearity and uncertainty in many applications, including those in the field of process systems engineering. But despite the apparent importance of such problems, the solution algorithms for these problems have found few applications due to the severe computational and structural restrictions. To that effect, this work proposes a new algorithm for a computationally efficient solution of the SNLP problems. Starting with the basic structure of the traditional L-shaped method, the new algorithm, called the L-shaped BONUS, incorporates the reweighting scheme to ease the computational load in the second stage recourse function calculation. The reweighting idea has previously been successfully used in optimization in BONUS, also an algorithm to solve the SNLP problems. The proposed algorithm is analyzed using different case study problems, including a blending problem relevant to the process industry and a large scale, novel sensor placement problem for water security networks. The results for all the problems show considerable savings in the computational time without compromising the accuracy, the performance being better for the Hammersley sequence sampling technique as compared to the Monte Carlo sampling technique. (c) 2006 Elsevier Ltd. All rights reserved.