Let \(X(t)\), \(t \in R^d\), \(d \geq 1\), be a real-valued Gaussian field with mean zero. Lower bounds on the small ball probability, i.e. \(P(\sup_{0 \leq t \leq 1} |X(t)|\leq x)\) for small \(x\)'s, are given for two classes of processes: Gaussian fields satisfying \(E |X(s) - X(t)|^2 \leq \sigma^2(|s - t|)\) for some nondecreasing function \(\sigma(x)\) and for Brownian sheet type Gaussian fields. Both estimates are sharp in certain cases. Namely, for fractional Lévy Brownian fields, i.e. \(E|X(s) - X(t) |^2 = |s - t|^\gamma\), \(0 < \gamma < 2\), it is found the upper bound which is of the same order as the lower bound obtained for the first class of processes. Also, the bound for the second class is sharp for a standard Brownian sheet at least when \(d = 2\).