A fitted mattress covering includes a body and an elastic strip. The body includes an upper surface and a side portion extending therefrom. The upper surface and the side portion together define a cavity therebetween shaped to receive a mattress. The side portion defines a lower edge of the body. The elastic strip is attached to the lower edge of the body and extends across and/or around a portion of the cavity. The elastic strip includes an inwardly-facing surface facing into the cavity and an outwardly-facing surface facing away from the cavity. At least part of one or both of the inwardly-facing surface and/or the outwardly-facing surface includes a non-slip portion. The non-slip portion is configured to generate a higher coefficient of friction with an adjacent surface than the elastic strip would provide without the non-slip portion.