Kuivalainen, who started for the Ilomantsin Urheilijat , ran her first individual World Cup races at the Winter Olympics in February 1984 in Sarajevo . She achieved 37th place over 10 km and 29th place over 20 km. In March 1988 she got her first World Cup point in Rovaniemi with the 15th place over 10 km freestyle and also won there with the relay. In the 1988/89 season she took third place in La Féclaz with the relay and at the Nordic World Ski Championships in 1989 in Lahti 27th place over 10 km freestyle. In the 1989/90 season she came in Thunder Bay over 15 km classic again on the 15th place and thus achieved her best individual result in the World Cup. In addition, she was in the season in Lahti and in Örnsköldsvik each third with the relay. She completed her 12th and last individual World Cup race in November 1995 in Vuokatti , which she finished classically in 69th place over 5 km.