Finite dimensional (FD) models, i.e., deterministic functions of space depending on finite sets of random variables, are used extensively in applications to generate samples of random fields
Z
(
x
)
Z(x)
and construct approximations of solutions
U
(
x
)
U(x)
of ordinary or partial differential equations whose random coefficients depend on
Z
(
x
)
Z(x)
. FD models of
Z
(
x
)
Z(x)
and
U
(
x
)
U(x)
constitute surrogates of these random fields which target various properties, e.g., mean/correlation functions or sample properties. We establish conditions under which samples of FD models can be used as substitutes for samples of
Z
(
x
)
Z(x)
and
U
(
x
)
U(x)
for two types of random fields
Z
(
x
)
Z(x)
and a simple stochastic equation. Some of these conditions are illustrated by numerical examples.