Developing new areas for burial at the two main cemeteries and creating a new cemetery.
Committee chair councillor Brian Finn, Labour, said: "Providing quality services for the bereaved is critically important but often doesn't get the profile it deserves.
The council is being urged to take action
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"In an era of huge demands on resources and land, bereavement must not be allowed to slip down our list of priorities. "
Cardiff council deals with over 4,000 funerals each year and more than 700,000 people visit its cemeteries and crematorium. More than 2,500 cremations take place each year.
The city is ranked 22 out of 82 in the Institute of Cemetery and Crematorium Management's league table of authorities providing burial and cremation services.
The report says burial space capacity has "reached a near-critical point" - a situation made worse by the increase in the population of Cardiff by 95,000 since the last cemetery - at Thornhill - was opened in 1953.
It points out that, although the council's Unitary Development Plan (UDP) makes reference to the need for additional cemetery space, it makes no commitment to build one.
At present, Cardiff Council does not allow the re-use of old graves, though other authorities have had to do so to cope with demands.
Conservative councillor Jon Burns said: "It is very clear the current situation is unsustainable as the report has highlighted.
"The council will need to think long and hard about viable alternatives for burial sites."
Plaid councillor Delme Bowen said: "The upgrading at Thornhill is long overdue both in respect of the improvement of quality and capacity."