A method of computer modeling a reservoir using multiple-point statistics from non-stationary training images is provided. Some methods include: a) identifying a path via a computer processing machine to visit all nodes of a simulation field; b) setting a template for searching data event in the simulation field and for searching data event replicates in the non-stationary training image; c) defining a neighborhood in which the training image is sampled; d) formulating a kernel function that gσ(d) that decreases from 1 to 0 when distance d increases from 0 to infinity; e) for the current node in the simulation filed, identifying the data event covered by the template; f) randomly sampling the training image in the neighborhood of corresponding node in the training image until an exact or approximate replicate of the data event is found; g) computing distance d between central node of the replicate and simulation node; h) computing the kernel function; i) drawing a random number u between 0 and 1; j) assigning value of central node of the replicate to the simulation node if gσ(d) is greater than u; k) repeating steps f) to j) if gσ(d) is not greater than u; and repeating steps e) to k) until all simulation nodes are visited