Black, the Paisley and Renfrewshire South MP, said she is regularly called a "wee boy" and told she wears her dad's suits, adding her and her pals laugh about this level of insults.
She said: "I struggle to see any joke in being systematically called a dyke, a rug muncher, a slut, a w****, a scruffy bint.
"I've been told you can't put lipstick on a pig, let the dirty b**** each s*** and die.
"I could soften some of this by talking about the C-word but the reality is there is no softening when you're targeted with these words and you're left reading them on my screen every day, day in, day out - she needs a kick in the c***, guttural c***, ugly c***, wee animal c*** - there is no softening just how sexualised and misogynistic the abuse is."
Black said she received a comment from a man she had never heard of before which said "I've pumped some ugly birds in my time but I just wouldn't".
She added: "I've been assured multiple times that I don't have to worry because I am so ugly that no one would want to rape me.
"All of these insults have been tailored to me because I am a woman."
Black said it is not simply "a few bad anonymous people on Twitter", adding: "But it's not. This is every day common language."
She said she felt uncomfortable reading out the insults, adding: "Yet there are people who feel comfortable flinging these words around every day.
"When it goes unchallenged it becomes normalised - and when it becomes normalised it creates an environment that allows women to be abused, ranging from a whole spectrum."
Women's Minister Atkins says she came off Twitter because she "got fed up with the abuse".
She told women: "You don't have to be on Twitter if you don't want to be."
Melanie Onn said catcalling at women should be treated in the same way as racism and homophobia.
Onn, a Labour shadow communities minister and MP for Great Grimsby, will argue that a change in the law would give women the confidence to report misogynistic behaviour.
Ahead of the debate she told the Grimsby Telegraph: "I've been told by police that women don't necessarily report these incidents, such as men standing far too close to them on public transport.
"In my experience, the first thing you do in that situation is doubt yourself that it is even happening. And even when you know it is, you don't know if the perpetrator will react aggressively if you do confront them about it.
"This could also include someone who catcalls a woman in the street or follows a woman out of a shop to chat them up when it is unwanted.
"I think these are warning signs and this change would give women the confidence to report these things.
"These things might be considered 'banter' or flirtatious but, if they are received as unwelcome in the way it is delivered, then it can be tantamount to harassment, even in a one-off case."
