After thoroughly studying the inherent qualities of leather socks, our illustrious Fuqaha suggest that non-leather socks should resemble leather socks in the following:

1.   They should entirely cover both the ankles.
2.   Both socks should independently be free from holes to the extent of three small toes.
3.   They should be durable enough that a person can walk with the sock for three miles without them tearing.
4.   The socks should remain on the leg without it being tied or fastened.
5.   They should be such that water does not seep through them when water is poured over them.

[Al Mabsoot lil Sarakhsi (1/18, 184 Dar al Fikr), Al Muheet al Burhani (1/343, Al Majlis al Ilmi), Ahkam al Quran lil Jassaas (3/440, Dar al Kutub al Ilmiyyah), Tuhfa al Mulook (1/33, Dar al Bashaair al Islamiyyah), Majma al Anhur (1/75, Dar al kutub al Ilmiyyah), Al Bahr ar raaiq (1/191, 192 Dar al Ma’rifah), Tabyeen al haqaaiq (1/52 Dar al kutub al Ilmiyyah), Al Fatawa al Hindiyyah (1/32, Dar al fikr), Ad Dur al Mukhtaar (1/269, Dar al fikr), Tuhfa al Ahwadhi (1/278, Dar al kutub al Ilmiyyah), Al Maslak adh Dhaki (1/29, Wajidi Publishers), Fatawa Mahmoodiyyah (5/195, Farooqiyyah), Fatawa Haqqaniyyah (2/216, Dar al Uloom Haqqaniyyah), Kifayah al Mufti (2/321), Farouqiyyah, Fatawa Darul Uloom Zakariyyah (1/509-5516, Zam Zam Publishers)]