The evolution and propagation of coronal mass ejections (CMEs) in interplanetary space is still not well understood. As a consequence, accurate arrival time and arrival speed forecasts are an unsolved problem in space weather research. In this study, we present the ELlipse Evolution model based on HI observations (ELEvoHI) and introduce a deformable front to this model. ELEvoHI relies on heliospheric imagers (HI) observations to obtain the kinematics of a CME. With the newly developed deformable front, the model is able to react to the ambient solar wind conditions during the entire propagation and along the whole front of the CME. To get an estimate of the ambient solar wind conditions, we make use of three different models: Heliospheric Upwind eXtrapolation model (HUX), Heliospheric Upwind eXtrapolation with time dependence model (HUXt), and EUropean Heliospheric FORecasting Information Asset (EUHFORIA). We test the deformable front on a CME first observed in STEREO-A/HI on February 3, 2010 14:49 UT. For this case study, the deformable front provides better estimates of the arrival time and arrival speed than the original version of ELEvoHI using an elliptical front. The new implementation enables us to study the parameters influencing the propagation of the CME not only for the apex, but for the entire front. The evolution of the CME front, especially at the flanks, is highly dependent on the ambient solar wind model used. An additional advantage of the new implementation is given by the possibility to provide estimates of the CME mass.