Electromagnetic transients program (EMTP) is widely used to analyse transients in power systems. With the increasing interest in integrated energy systems (IESs), it would be beneficial to extend the application of EMTP to multi-physics transients in integrated electrical and heating networks. In this paper, an accurate and efficient lumped-element circuit model of the heating district pipe is developed in EMTP. The pipe is split into segments using spatial discretisation. The application of the numerical discretisation to the energy conservation equation gives the discretised pipe equation which is expressed in the form of a companion model of EMTP. In order to reduce the computational effort, the time-varying terms in the admittance matrix of the companion model of pipe are eliminated. The modification of the admittance matrix is avoided. Furthermore, the internal nodes resulting from spatial discretisation are eliminated, and the pipe model appears as a lumped-element circuit with two external nodes. Case studies are carried out to verify the accuracy and efficiency of the proposed lumped-element circuit model of pipe. The implementation of the proposed pipe model in the EMTP-type simulator enables the analysis of multi-physics transients in a multi-carrier energy system.