In the late 1930's the softer silhouette retained a Grecian style for many evening style. This gown is probably a silk charmeuse. It gathers up the center front into a narrow placket and skirt fullness is released at the end of that placket. The draped sleeves have a bit of fullness to give her shoulders fashionable width.
I don't have the date or source, this picture is from an undated fashion scrapbook.