In this paper a brief introduction to the theory of stochastic vector and tensor fields is given. Necessary and sufficient conditions for isotropic vector random fields are reviewed and necessary conditions for second order tensors are developed. These models increase the flexibility of the usual geostatistical models but at the cost of increased complexity. This complexity can be reduced to a manageable level for a class of tensor fields that are associated with strain. The potential for modelling fractures using strain models is briefly discussed.