A rain gutter filter apparatus and method utilize a filter element of a reticulated foam material adapted for insertion into a gutter having an open top defining a top width of the gutter. The filter element has a flat top surface with a width substantially matching the top width of the gutter, a bottom surface having a width less than the top width of the filter element, and front and rear surfaces extending upward from the bottom surface of the filter element to thereby form a front and a rear open passage for water on front and rear sides of the bottom surface of the filter element when the filter element is installed into the gutter. The reticulated foam material of the filter element has a composition that is flame resistant, germicidal, mold resistant, and resistant to degradation by exposure to ultraviolet rays.