Solid-state cooling technology based on the caloric effects of phase-transition materials has been a research hotspot due to its environmental friendliness and high efficiency, but limited for practical applications due to its narrow working temperature region. Here, we report giant barocaloric effects based on pressure-driven liquid-solid phase transitions in elastic copolymers of ethylene and vinyl acetate. Giant adiabatic temperature changes of up to 29.6/-26.9 K are directly observed under rapid compressions/decompressions of 400 MPa near the liquid-solid phase transition points. Strikingly, since both the solid and the liquid sides can show giant barocaloric effects, a very broad refrigeration temperature region of more than 110 K is achieved in these copolymers. Furthermore, a cooling prototype is designed to demonstrate the potential applications of these liquid/elastic barocaloric materials. Our study sheds light on exploring liquid-solid phase transition materials for the next-generation refrigerators.