Three-dimensional printing could be used to create complex and multifunctional soft electronic devices. However, printing solid-state elastic conductors with three-dimensional geometries is challenging because the rheological properties of existing inks typically only allow for layer-wise deposition. Here we show that an emulsion system—consisting of a conductive elastomer composite, immiscible solvent and emulsifying solvent—can be used for the omnidirectional printing of elastic conductors. The viscoelastic properties of the composite provide structural integrity to the printed features—allowing freestanding, filamentary and out-of-plane three-dimensional geometries to be directly written—and pseudo-plastic and lubrication behaviours that provide printing stability and prevent nozzle clogging. Printed structures of the intrinsically stretchable conductor exhibit a minimum feature size less than 100 μm and stretchability of more than 150%. The vapourisation of the dispersed solvent phase in the emulsion results in the formation of microstructured, surface-localized conductive networks, which improve the electrical conductivity. To illustrate the capabilities of our approach, we create a skin-mountable temperature sensor with a matrix-type stretchable display based on omnidirectionally printed elastic interconnects. Freestanding, out-of-plane structures made of stretchable conductors can be printed using an emulsion-based ink that has the viscoelasticity to be extruded into three-dimensional geometries and supporting its own shape.