This article presents an analytical approach to estimate the background component of diffuse irradiance on vertical surfaces under partially obstructed anisotropic sky, when neighbor orthogonal vertical and horizontal surfaces hide parts of the sky dome. This helps to calculate the incident diffuse radiation onto the facades of orthogonal buildings using defined here vertical and horizontal anisotropic sky view factors. The cases of infinitely long urban canyons and infinitely high vertical walls also are studied. The resulting equations include an isotropic part and an anisotropic correction. At last the article describes the fundamental relations between anisotropic sky view factors, which form base of anisotropic factor algebra. (C) 2013 Elsevier Ltd. All rights reserved.