A new Lagrangian particle method for solving transient viscoelastic flow for both macroscopic and microscopic stress equations is proposed. In this method, referred to as the backward-tracking Lagrangian particle method (BLPM), we specify the particle locations and calculate the trajectories leading to these locations. This backward tracking process is stopped after a specified time (possibly only a single time step), and the initial configuration for the Lagrangian integration of the stress is obtained by interpolating a stored Eulerian field at that time. In order to demonstrate the accuracy, efficiency and stability of the method, we consider two benchmark problems in the context of the FENE dumbbell kinetic theory of dilute polymer solutions and its FENE-P approximate constitutive equation: the high eccentricity journal bearing flow and the 4:1 contraction flow. With the help of these examples, we show in which manner accurate and stable results can be obtained, for transients of both polymer stress and stream function, with a minimum number of particles and a minimum particle path length.