Summary: The article deals with isolated essentially singular points of analytic functions The basic result states that if an essentially singular point z0 of an analytic function f is an isolated singular point of the corresponding plane vector field  then the function can be represented in the form f<(z) = (z - z0)n g (z) exp h ((z - z0)-1) where n is an integer (coinciding with the Poincare index of z0)  g is an analytical function in a neighborhood of z0 with g (z0) ¹ 0  and h is an entire function with h(0) = 0