The accurate analysis of Log–Normal power–sums requires the computation of multidimensional integrals with unknown closed–form. Typical approaches to numerically com- pute them are based on the full tensor–product formula, whose complexity raises exponentially with the number of summands. In this Letter, we propose a different method which is called Smolyak’s algorithm. It belongs to the family of numerical integration techniques on sparse grids, and can be used in conjunction with several approximation methods for Log–Normal power–sums. Numerical results will show a complexity reduction greater than 99% without numerical accuracy degradation.