In this paper we study the numerical solutions of the stochastic functional differential equations of the following form $$du(x,;t);=;f(x,;t,;u_t)dt;+;g(x,;t,;u_t)dB(t),;t;>;0$$ with initial data $u(x,;0);=;u_0(x);=;{xi};{in};L^p_{F_0};([-{ au},0];;R^n)$. Here $x;{in};R^n$, ($R^n$ is the ${ u};-;dimenional$ Euclidean space), $f;:;C([-{ au},;0];;R^n);{ imes};R^{{ u}+1};{ ightarrow};R^n,;g;:;C([-{ au},;0];;R^n);{ imes};R^{{ u}+1};{ ightarrow};R^{n{ imes}m},;u(x,;t);{in};R^n$ for each $t,;u_t;=;u(x,;t;+;{ heta});:;-{ au};{leq};{ heta};{leq};0;{in};C([-{ au},;0];;R^n)$, and B(t) is an m-dimensional Brownian motion.