The unpublished report for the Health Service Executive shows the number of cases doubled since 2007, when the figure was 927 cases.
Nearly two-thirds of those believed to be affected last year were female.
In 26% of cases, the alleged abuse was classified as psychological, in 19% of cases it involved neglect, 16% financial matters and in 12% physical abuse.
The type of abuser was consistent across all regions and usually involved a person with the closest relationship to the older person, such as a son, daughter, partner or spouse.
The breakdown by region of cases reveals that the south accounted for 47% of referrals, Dublin northeast 23%, the west 17% and Dublin mid-Leinster 13%.
The high rate in the south is partly accounted for by the fact there were 160 cases there of individuals being re-referred to the HSE.
Nationally, the person most likely to report a case was a public health nurse, hospital or HSE staff member.
Referrals by family accounted for less than 15% of cases.
At the end of last year, 54% of cases remained open, while the remainder were closed, having been determined as inconclusive or not substantiated.
The HSE now has dedicated officers for elder abuse in each administrative area.
