As of the census of 2000, there were 18,842 people, 6,081 households, and 4,907 families residing in the county. The population density was 10 people per square mile (4/km²). There were 7,016 housing units at an average density of 4 per square mile (1/km²). The racial makeup of the county was 95.61% White, 0.27% Black or African American, 2.00% Native American, 0.26% Asian, 0.09% Pacific Islander, 0.79% from other races, and 0.99% from two or more races. 2.55% of the population were Hispanic or Latino of any race.
There were 6,081 households out of which 43.00% had children under the age of 18 living with them, 70.10% were married couples living together, 7.80% had a female householder with no husband present, and 19.30% were non-families. Of the 6,081 households in Sevier County, 155 are unmarried partner households: 137 heterosexual, 11 same-sex male, and 7 same-sex female. 17.60% of all households were made up of individuals and 9.40% had someone living alone who was 65 years of age or older. The average household size was 3.03 and the average family size was 3.44.
In the county, the population was spread out with 34.50% under the age of 18, 10.10% from 18 to 24, 22.90% from 25 to 44, 19.70% from 45 to 64, and 12.90% who were 65 years of age or older. The median age was 30 years. For every 100 females there were 99.20 males. For every 100 females age 18 and over, there were 97.40 males.
The median income for a household in the county was $35,822, and the median income for a family was $40,110. Males had a median income of $32,632 versus $19,228 for females. The per capita income for the county was $14,180. About 8.30% of families and 10.80% of the population were below the poverty line, including 12.80% of those under age 18 and 8.50% of those age 65 or over.