1.6. Permissability of reciting the Quran whilst one is standing, walking, riding, sitting or lying down

الَّذِينَ يَذْكُرُونَ اللّهَ قِيَامًا وَقُعُودًا وَعَلَىَ جُنُوبِهِمْ
Those who remember Allâh standing, sitting, and lying down on their sides... (Aali Imran 3:191)

لِتَسْتَوُوا عَلَى ظُهُورِهِ ثُمَّ تَذْكُرُوا نِعْمَةَ رَبِّكُمْ إِذَا اسْتَوَيْتُمْ عَلَيْهِ وَتَقُولُوا سُبْحانَ الَّذِي سَخَّرَ لَنَا هَذَا وَمَا كُنَّا لَهُ مُقْرِنِينَ
وَإِنَّا إِلَى رَبِّنَا لَمُنقَلِبُونَ
In order that you may mount firmly on their backs, and then may remember the Favour of your Lord when you mount thereon, and say: "Glory to Him who has subjected this to us, and we could never have it (by our efforts). And verily, to Our Lord we indeed are to return! " (Az-Zukhruf 43:13-14)

'Abd Allaah ibn Mughaffal (may Allah be pleased with him) said: I saw the Messenger of Allah reciting Soorah al-Fath while he was riding his camel. (Related by al-Bukhari and Muslim)

'Aa`ishah (may Allah be pleased with her) said: While I would be menstruating the Prophet would recline in my lap and recite the Quran.