After Thursday's hearing, a court-appointed rapporteur will prepare a non-binding report on what verdict the judges should give.
The court will then set a date to debate the case behind closed doors and reach a decision.
Name change option
Yalcinkaya launched the proceedings in March, arguing that the AKP had become a "focal point" of anti-secular activities aimed at installing an Islamist regime in Turkey.
He also asked the court to bar 71 AKP officials, including Recep Tayyip Erdogan, the Turkish prime minister, and Abdullah Gul, the president, from party politics for five years, in line with Turkish law.
Hoda Abdel-Hamid, Al Jazeera's correspondent in Ankara, Turkey's capital, said that if Erdogan is banned and the AKP is forced to shut down, the ruling party could in fact change its name and have a new leader, but with Erdogan pulling the strings from behind the scenes.
Many analysts have added that in the time between the hearings and the verdict - which could be months - Erdogan could call for general elections with the AKP changing its name and re-presenting itself.
According to one opinion poll, the majority of Turks do not favour banning the AKP.
The poll, published in the Milliyet newspaper on Monday, found that 53.3 per cent of those surveyed opposed a ban with 34.3 per cent in favour.
It also showed that the AKP is still the most popular party in the country despite the court proceedings.
The AKP won the last elections in July 2007 with 47 per cent of the vote and the next poll would not normally be due until 2011.