The greatest pressure is felt at the Swedish embassy in Cairo where it can take over a year to get an interview. Many of the refugees are eager to move to Sweden to be reunited with their family members who have already been granted asylum.
In September last year, Sweden granted permanent residence to all Syrian refugees, the first country in the EU to do so.
In the first five months of 2014 more than 8,000 Syrians, or stateless people, filed for asylum in Sweden. According to statistics quoted by Sveriges Radio, that figure is five times higher than the corresponding period of 2013.
"The reality is that there are two departments handling each case; the Swedish Foreign Ministry (Utrikesdepartementet) and the Swedish Migration Board (Migrationsverket) and there can be a long wait between submitting your application to the embassy or consulate before getting an interview. It is only after the initial interview that the application is sent to the Migration Board," Magnus Skarbo press information officer for the Swedish Migration Board told The Local.
He added that many embassies and consulates around the world are not suited to dealing with the sheer volume of applicants. Several embassies have hired new staff to cope with the demand with Migration Minister Tobias Billström saying that Sweden's willingness to bring in refugees has led to the backlog.
"It's one of the reasons why processing times are unfortunately so long," Billström told TT. He added that waiting times have not increased in recent months.
The Migration Board has been criticised in the past for taking too long to process the applications. It has since implemented changes to speed up the situation and to give priority to Syrian refugees.
"We have a special unit in Sweden that is just dealing with these cases of Syrian asylum seekers. At present there are no plans to start a new unit dealing specifically with applicants from Iraq or in Gaza," Skarbo told The Local.
He added; "The waiting times differ from embassy from embassy. Cairo is one where there is a lot of applicants. For the refugees it can be difficult as they can face a wait before being reunited with their families. From speaking to the people at the embassies I have a sense that they are calm and in control."
In June The Local reported that Sweden took almost 20 percent of the EU's asylum seekers, more than any other country in Europe. Of the asylum seekers in Sweden, 46 percent were from Syria.
The Swedish Migration Board recently raised its forecast for the number of refugees seeking help and protection in Sweden from 61,000 to 70-80,000 for 2014.
It is estimated that in excess of 20,000 Syrians could form almost a quarter of the entire refugee tally to come to Sweden.
A spokesperson for the Migration Board said it was doubtful that figures would decline in the coming years.