Kriging is of particular interest in network design because of its ability to estimate streamflow values using existing stations. Another possibility offered by kriging is the estimation of variance reduction gained by addition of fictitious stations in regions of high variance. In this article we give a brief description of kriging theory as developed at the Ecole des Mines de Paris. In order to improve and optimize the Quebec streamflow recording network design we kriged specific streamflows with a given return period over the Quebec province, using the data observed at existing stations. For the evaluation of the given return period flow and its sampling variance at each gauged site we use the log Pearson type 3 distribution model. Kriging is an optimal estimation technique, in terms of minimum variance, and contrary to other methods it gives an estimation variance for any point in the kriged domain, which is essential in network design.