A stretch of the National Highway 21, that passes through Mandi, has been closed fearing more landslides.
A Home Ministry official said that as many as seven teams of National Disaster Response Force (NDRF), comprising 45 personnel in each, have already reached the affected areas in Bihar.
So far, 10 bodies have been recovered from the debris.
One of the state roadways bus was hit by the landslide debris and skidded off the road, falling down by nearly a kilometre.
Iran's parliament votes to increase missile funds following United States sanctions
It came after the US House of Representatives and then the Senate passed a sweeping package of bills on sanctions against Iran, Russia, and North Korea.
According to witnesses, the two buses were stationed at a kiosk on the highway for refreshments when the incident took place. It swept away the buses 800 metres down into a gorge and buried one of the buses completely.
Confirming the development, Himachal Pradesh transport minister G S Bali said that around 50 people are feared to have been washed away in the incident.
At least 44 passengers died after a bus carrying them turned turtle and fell into River Tons in Himachal Pradesh's Gumma on Wednesday.
Deputy Commissioner of Mandi, Sandeep Kadam said, "Three vehicles were stranded after the landslide". As per a Times of India report, one of the bus was on its way to Katra in Jammu from Manali, while the other was on its way to Chamba from Manali.
Chief Minister Virbhadra Singh and Leader of Opposition Prem Kumar Dhumal rushed to the spot. "Immediate relief will be provided", Mr Singh said.