Multivariate descriptions of soil parameters are quite important for the design and risk assessment of geotechnical engineering problems. A reliable and realistic statistical multivariate model is essential to produce a representative estimate of the soil properties for evaluating the soil conditions. Therefore, an advanced modeling of soil parameters helps towards improving the geotechnical and civil engineering practices. In this paper, we introduce the concepts of asymmetric copulas for the modeling of geotechnical data. Several asymmetric copula functions, capable of modeling nonlinear asymmetric dependence structures, are tested and analyzed. To demonstrate the advantages of asymmetric copulas, the asymmetric copula concept is compared with the traditional copula approaches from the real collected site soil data. The performance of these asymmetric copulas is discussed and compared, based on data fitting and tail dependency characterizations.