Nearly 330 patients were admitted through the accident and emergency department at Naas Hospital during May without a bed being available.
The figure of 329 is the highest for May since 2011.
The highest ever overcrowding figure for May was in 2011 when 524 people were admitted on trolleys.
According to the Irish Nurses and Midwives Organisation, which compiles the figures, the overcrowding problem was worse last month than any other May since the compilation of figures started in 2006.
The figure for May has increased from 4214 to 9091 between 2006 and 2018.
The INMO has, predictably, criticised the overcrowding problem.
It said the figures (nationally) show an overall increase of 12% on May 2017 and overcrowding is an increasing problem year on year and is a feature of patient care throughout the whole twelve months.
It also said hospitals are constantly overworked and “working above the recognised safe occupancy level and demand for emergency admissions, even in the peak summer period, continues to grow.”
Phil Ní Sheaghdha, the INMO's general secretary, said the so-called winter initiative needs to be reexamined as a solution to this “constant and worsening crisis”.
She added that funding should not be left until late N ovember of January “when the escalating problems are out of control.”
Ms Ni Sheaghdha added: “We live in a society which expects a long wait and a lack of privacy and dignity when attending emergency departments.”
She added this is not acceptable and it is a basic human right that a person deemed as requiring hospital admission is admitted to a suitable bed which is appropriately staffed.