The human rights group says weapons are all too often being used against civilians or they end up in the hands of groups opposed to the government.
There is currently an arms embargo in place for Somalia.
But with UN approval weapons have been delivered to the government which is under attack from Islamist militants.
Somalia is awash with weapons already, and there are many armed groups fighting for power.
But as the international community tries to prop up the beleaguered transitional government, more and more weapons are being sent in.
Last year, the United States delivered 19 tonnes of weapons and ammunition and may have sent a lot more as other requests for exemptions to the arms embargo were made.
Amnesty International wants arms transfers to the Somali government suspended because it says these weapons are used in indiscriminate attacks against civilians, especially when mortars are fired.
It also says some of the weapons end up in the hands of militias fighting against the government – partly as a result of troops defecting from one side to another.
The Somali government is protected by several thousand African Union troops, without whom many analysts believe the government would not be able to survive.
But there are efforts to boost the long-term capacity of the pro-government soldiers and police.
The US, European Union countries and several east African nations have pledged or are already delivering training to more than 20,000 of these forces.
Amnesty International says that all sides in Somalia’s conflict have been committing human rights abuses, and it therefore says it is essential that international humanitarian law be part of any training that is given.
Whilst the transitional government has widespread international backing, several countries including Eritrea have been accused of funding and arming the opposition hardline Islamist groups like al-Shabab. Last month, the UN Security Council imposed an arms embargo on Eritrea.
It will however be incredibly hard to stop the inflow of weapons to Somalia.
And there is as yet no sign that the civilians will have any respite from the fighting which has displaced 1.5 million people.