Plains is located at 37°15'45N, 100°35'30W (37.262633, -100.591681). According to the United States Census Bureau, the city has a total area of 2.6 km² (1.0 mi²), all land.
As of the census of 2000, there were 1,163 people, 402 households, and 303 families residing in the city. The population density was 453.6/km² (1,175.8/mi²). There were 453 housing units at an average density of 176.7/km² (458.0/mi²). The racial makeup of the city was 82.12% White, 1.29% Native American, 14.27% from other races, and 2.32% from two or more races. Hispanic or Latino of any race were 26.23% of the population.
There were 402 households out of which 43.5% had children under the age of 18 living with them, 64.7% were married couples living together, 7.0% had a female householder with no husband present, and 24.4% were non-families. 22.1% of all households were made up of individuals and 10.7% had someone living alone who was 65 years of age or older. The average household size was 2.89 and the average family size was 3.41.
In the city the population was spread out with 34.5% under the age of 18, 10.1% from 18 to 24, 27.6% from 25 to 44, 16.3% from 45 to 64, and 11.6% who were 65 years of age or older. The median age was 28 years. For every 100 females there were 102.6 males. For every 100 females age 18 and over, there were 101.1 males.
The median income for a household in the city was $39,688, and the median income for a family was $44,167. Males had a median income of $31,354 versus $21,023 for females. The per capita income for the city was $16,047. About 11.4% of families and 13.6% of the population were below the poverty line, including 19.3% of those under age 18 and 0.9% of those age 65 or over.