Neversink is a town in Sullivan County, New York, United States. The population was 3,557 at the 2010 census.
Part of the town is in the Catskill Park. The northern and eastern town lines are on the border of Ulster County, New York.
According to the United States Census Bureau, the town has a total area of 86.4 square miles (224 km), of which, 82.9 square miles (215 km) of it is land and 3.5 square miles (9.1 km) of it (3.99%) is water.
As of the census of 2000, there were 3,553 people, 1,346 households, and 1,008 families residing in the town. The population density was 42.8 people per square mile (16.5/km²). There were 1,960 housing units at an average density of 23.6 per square mile (9.1/km²). The racial makeup of the town was 96.93% White, 0.56% African American, 0.23% Native American, 0.23% Asian, 0.65% from other races, and 1.41% from two or more races. Hispanic or Latino of any race were 2.20% of the population.
There were 1,346 households out of which 35.7% had children under the age of 18 living with them, 61.3% were married couples living together, 9.3% had a female householder with no husband present, and 25.1% were non-families. 21.0% of all households were made up of individuals and 8.7% had someone living alone who was 65 years of age or older. The average household size was 2.64 and the average family size was 3.06.
In the town, the population was spread out with 28.1% under the age of 18, 5.6% from 18 to 24, 28.7% from 25 to 44, 25.4% from 45 to 64, and 12.2% who were 65 years of age or older. The median age was 38 years. For every 100 females, there were 96.1 males. For every 100 females age 18 and over, there were 95.4 males.
The median income for a household in the town was $45,174, and the median income for a family was $55,075. Males had a median income of $40,744 versus $22,031 for females. The per capita income for the town was $19,260. About 8.7% of families and 11.3% of the population were below the poverty line, including 14.3% of those under age 18 and 13.7% of those age 65 or over.