More than a dozen people died in the state's Rudraprayag district alone, while another 50 people were missing, said Amit Negi, an official in Uttarakhand.
A landslide triggered by the monsoon rains buried a bus, killing three people in Almora district.
At least three other people were washed away when a three-story apartment building toppled into a river and was carried away by the swift-moving current, said Amit Chandola, a government spokesman.
More than 10,000 pilgrims stranded along a mountain pass leading to a Hindu religious site were being evacuated by helicopter after roads to the pilgrimage spot were blocked by landslides.
Army and paramilitary troops were leading efforts to rescue scores of people from the rooftops of their flooded homes. The state government was readying food parcels and drinking water pouches to be air dropped to villages cut off after roads were washed away.
The River Ganges and its tributaries are flowing above the danger mark in several areas in the Himalayan state.
"The situation is very grim. The meteorological office has predicted that the rain will continue for another three days at least," said Chandola.
State authorities were preparing to evacuate people from the worst-hit districts to relief camps, he said.
A high alert and flood warnings have been issued across Udhampur district and in the Hindu holy city of Haridwar as rivers breached their banks.
Flooding is an annual occurrence in India, which depends on monsoon rains for agriculture. The heavy downpours often cause loss of life and property.