A mathematical model of the tumour growth along a blood vessel is proposed. The
model employs the mixture theory approach to describe a tissue which consists of cells, extracellular
matrix and liquid. The growing tumour tissue is supposed to be surrounded by the host
tissue. Tumours where complete oxydation of glucose prevails are considered. Special attention is
paid to consistent description of oxygen consumption and growth processes based on the energy
balance. A finite difference numerical method is proposed. The level set method is used to track
an interface between the tissues. The simulations show localization of the tumour within a limited
distance from the vessels and constant expansion velocity along the vessels.