No shops are open, and the city has had no electricity, gas or water since the Kakhovka Dam was blown up in 2023, flooding the area and killing many people in Oleshky itself.
The current truce is supposed to enable roads to be cleared of mines for supplies to get into the city possibly on Thursday, and for residents to have safe passage out in an evacuation planned for Friday.
Several thousand residents are trapped in the city with no access to food, water and electricity.
Under the deal, the ceasefire will be followed by deliveries of humanitarian aid to Oleshky and then evacuations, planned for Friday, for anyone wishing to leave.
Many details on the evacuation plans are unclear, and residents are wary of trusting officials with their names and addresses.
Many residents have resorted to cooking garden weeds to survive, telling the they are suffering extreme hunger and want to leave.
Across the river, in Kherson city, no explosions have been heard and no drone-related injuries reported since 03:00 (01:00 GMT) on Tuesday and cars and pedestrians have been moving freely, according to local reports.
An estimated 1,700 to 2,000 people remain in Oleshky itself and a few thousand more in surrounding areas.
Both sides said the ceasefire was being observed.