Materials with desirable properties, including good deformability, high thermal conductivity, and superior electromagnetic interference (EMI) shielding, are in high demand in the modern electronics sector. In order to overcome fundamental heat transport and EMI shielding limitations in soft elastic materials, liquid metal (LM) is dispersed randomly in self-healing polyurethane (SPU) to produce composites with high thermal conductivity and excellent EMI shielding properties preserving the softness and deformability of the precursor. Furthermore, stretching-induced filler alignment method is utilized to elongate and align the LM in the SPU matrix along the draw direction, resulting in simultaneous enhancement in the in-plane thermal conductivity and the EMI shielding effectiveness (SE) of the composites. LM/SPU composites with 80 wt% filler loading show the in-plane thermal conductivity as high as 12.8 W·m-1·K-1 and total EMI SE of 72 dB, respectively, at the draw ratio of 3. Excellent deformability of the LM facilitates its alignment in the composites along the stretching direction, which makes phonon transfer easier and allows for multiple reflections and absorption of electromagnetic waves, which greatly enhances thermal conductivity and EMI shielding. In addition, the prepared LM/SPU composites show excellent healing properties. Therefore, this study provides a promising strategy for integrating multifunctional properties into a single composite system for application in flexible electronics.