Our goal in the present work is to give an insight on some important questions to be asked when choosing a kriging model for the analysis of numerical experiments. We are especially concerned about the cases where the size of the design of experiments is small relatively to the algebraic dimension of the inputs. We ¯rst ¯x the notations and recall some basic properties of kriging. Then we expose two experimental studies on subjects that are often skipped in the ¯eld of com- puter simulation analysis: the lack of reliability of likelihood maximization with few data, and the consequences of a trend misspeci¯cation. We ¯nally propose a case study, with the application of an original kriging method where an additive model is used as external trend.