The article studies the ritual meaning of the sed-festival run and localisation of a place where this run might have taken place while performed by rulers of Early Dynastic Egypt. The first part of the article is devoted to the study of the sed-festival. The author expresses his doubts concerning the opinion that originally heb-sed was a festival of the renewal of the king’s potency. From the author’s point of view, the rise of the state and that of the sed-festival may be connected. In fact, intensive analysis of the sources shows that the sed-festival came into being at the dawn of dynastic history as a military celebration held after the successful suppression of revolts in the Delta and re-unification of the country under the power of a strong monarch. The heb-sed run of a pharaoh was a culmination point of the sed-festival celebration in all periods of ancient Egypt history. The ruler is usually depicted as performing his run between semi-circular, horseshoe-like signs reminding of the letter D. They are called dnbw in hieroglyphic texts. The author assumes that the dnbw signs were associated by ancient Egyptians with the southern and northern borders of the country. In this case the territory limited by them could be conceived as the whole of Egypt. The run between dnbw signs also has the meaning of Upper and Lower Egypt’s unification. At the same time it demonstrated physical strength of the ruler. The author believes that triple repetition of the horseshoe-shaped sign on the depictions of the sed-festival run presumably expresses the idea of plurality of objects rather than indicates their exact number. Thus if we mentally continue those sets of signs and than enclose them from both sides the received picture will be identical to the representation of an early dynastic city surrounded by a protective wall. In this case horseshoe signs could be nothing but a symbolic image of towers of the city walls around which a pharaoh was making his run. The author presumes that originally during the sed-festival a pharaoh made a ritual run around the walls of city rather than of the City par excellence, i.e. Memphis, which became capital of the state at the accesion of the I dynasty. The second part of the article is devoted to the localization of the «White Walls» which were the object of circumambulation during the sed-festival run. The author believes that in the Early Dynastic period and during the III Dynasty rule the core of Memphis lay in the northern part of the present day Memphis site, on the territory which bears the modern Arabic name of Kom Tuman. The Center for Egyptological Studies of the Russian Academy of Sciences is currently conducting archaeological excavations in this area. The author also argues that some palatial installations of the III dynasty were situated in the area of Kom Tuman. Although it is a very speculative idea, it follows the pattern of the city development. The site is located almost opposite the Djoser and Sekhemhet mortuary complexes. The author believes that the architectural layout of the pharaoh Apries’ palatial complex at Kom Tuman copied main features of the Djoser mortuary complex which in its turn imitated in stone the residence of the first ruler of the Old Kingdom built of perishable material. The ideology of the XXVI dynasty would fit very well into this spatial symbolism. Later on after the fall of Apries, the Kom Tuman area did not lose its status as the governmental center of the Memphite city. We may presume that under the rule of Amasis, colonies of Carian and Ionian mercenaries were settled there beside the Apries palace. It remained the main stronghold of the city under the Persian dominance in Egypt. Most probably the Apries palace and a camp surrounded by an enclosure wall were the White Fortress (Leukon Teikhos), where, according to Herodotus, a Persian garrison was disposed.