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Electromagnetic transients program (EMTP) is widely used to analyze transients in power systems. With the increased 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 discretization. The application of the numerical discretization to the energy conservation equation gives the discretized 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 discretization are eliminated, resulting in a lumped-element circuit model with only two external nodes. Case studies are carried out to validate the proposed model in terms of accuracy and efficiency. The 2-norm error of the proposed model is 0.0153%. With a pipe length of 100 m, the computational speed of the proposed model is increased by a factor of 2.94 compared with the existing distributed-element circuit model. 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. [ABSTRACT FROM AUTHOR]