The Mirror have reported that two separate families were allowed to board the wrong flight.
The Pritchards and the Housleys had booked to fly to Almeria in Spain, leaving from East Midlands Airport in the UK.
But both families say they were ushered onto a plane for Riga, Latvia, which is 2,000 miles away.
Their boarding passes were checked three times before they got to their seats and it was only when the real occupants arrived that the mistake was realised.
The Pritchards were too late to get their intended flight and had make their own way to Birmingham airport to get the next available flight to Spain which was 10 hours later.
They blame Ryanair staff at East Midlands Airport for not realising they were getting onto the wrong flight, even though their boarding cards and details were checked numerous times.
It is believed that the confusion ma have arisen when two queues formed close to one another at two different boarding gates.
A spokesman for Ryanair made a statement on the situation: ''While it is the responsibility of each customer to ensure they board the correct aircraft, we have asked our handling agent at East Midlands to investigate this incident and ensure it does not recur.
"We sincerely apologise to the customers in question, who have been transferred onto the next available flight free of charge, provided with refreshment vouchers and advised to keep receipted expenses for reimbursement of additional transport costs."