Approaching Storm is among the many landscape paintings Eilshemius made of American locations he visited on numerous sketching trips in the 1880s and 1890s. Returning to the favorite haunts of the Hudson River school painters—the Adirondacks, the Delaware Water Gap, and the shores of the Hudson River—Eilshemius painted in a style influenced by his first teacher, Robert Minor, and the French Barbizon school. Duncan Phillips said that Eilshemius's landscapes possessed the "lyrics of light and color and perfect atmospheric values which are worthy of comparison with George Inness and even Corot, especially the early Corot." In addition, he noted the artist's tendency to use a tonalist approach, describing his landscapes as "blonde...with their pearly skies, their thinly and directly painted woodland dells or translucent open spaces, their dark and slender trees, and their tiny little people, usually ladies and children."
Approaching Storm differs from the artist’s other landscape in that it is ominous and has eerie colors and intense contrasts of light and dark. The stormy atmosphere and surging, swaying forms of the landscape set up a threatening scenario for the tiny figures running about. The psychological tensions and emotional expressiveness of the painting separate it from the landscape traditions that had initially influenced Eilshemius. Duncan Phillips saw Eilshemius's paintings as a bridge between old and new, and as possessing the expressive power of El Greco and Van Gogh, prefiguring the "improvisations on nature" of Bonnard and Marin, and anticipating the "subjective abstraction" of Dove and Tack.