Beaumont will address an expected 3,000 riders converging on Holyrood for the seventh annual lobby to press for improved cycle safety.
He expected to say: "While I believe progress has been made over the past seven years to make Scotland a safer country to cycle in, it is massively important our MSPs understand how vital safer roads and better infrastructure are for everyone.
"It’s only through a mindset of sharing roads and respect for everyone that we will see more adults and children feeling safe enough to cycle as part of their everyday lives.”
The record-breaking long-distance cyclist is due to take part in the ride from The Meadows at noon in a cargo bike with his two young daughters.
Other speakers at the rally outside the Scottish Parliament - which deliberately do not include politicians this year - include Scotsman columnist Lesley Riddoch, Steven McCluskey and Yaman from Bikes for Refugees and Jean-Matthieu Gaunand from Edinburgh and Lothians Regional Equality Council.
There will be similar demonstrations in Inverness tomorrow and in Aberdeen on Sunday.
Neil Greig, the Scottish-based policy and research director of motoring group IAM RoadSmart, said: "We can all agree cycling will only really take off as more and more segregated facilities come on stream.
"In the meantime, Scottish drivers are sharing the road safely with the growing number of cyclists despite a totally unsuitable infrastructure in many places."
Beaumont's call for mutual respect comes five years after cycling campaigners criticised a Scottish Government-backed campaign on the issue called the Nice Way Code.
Lothian Green MSP Alison Johnstone, who is co-convener of the Scottish Parliament's cross-party cycling group, said a “considerable” number of constituents had complained to her that the campaign was “insulting and patronising”, while others found the adverts “misleading and even dangerous”.BACKGROUND: Inside Transport - Surprise cycling turnout could herald change
The Pedal on Parliament events will renew the campaign's call for 10 per cent of transport spending on cycling, lower speed limits and better enforcement of traffic laws.
Sally Hinchcliffe, one of the organisers, who will also speak at the event, said: “We’ve had enough of listening to politicians making assurances that things will improve.
We need to move beyond the soundbites and judge them based on their actions.
"The evidence is out there, and other cities across Europe are already taking action.
"We need our representatives to hear our voices and make our country safe for everyone who wants to ride their bike.”
Fellow organiser Alice Lyall said: “A few years ago I had a frightening fall on Princes Street when my bike wheel got trapped in the tram line.
"I was really lucky and walked away with a concussion.
"Since then, a young woman in Edinburgh has lost her life in a similar incident, and hundreds of other people have been hurt.
"It makes me angry sometimes - it shouldn’t feel this risky to get around my own city just because I’m not in a car.
"Our roads should be safe for all of us."
Denise Marshall, who is also taking part, said: “I always liked to use my bike instead of my car until I had children."
"Now, I worry about all the potholes and close passes.
“I really miss the fresh air and exercise just getting around town and I’m disappointed that I’ve had to stop for a while.”
The Inverness ride is at 11am tomorrow from Bellfield Park to Highland Council's headquarters., with speakers including Scottish Greens MSP John Finnie and SNP MP Drew Hendry.
The Aberdeen event on Sunday starts at 11am at Rubislaw Terrace Gardens on Albyn Place to the Town House on Broad Street, which will be addressed by Aberdeen University geography and environment lecturer Dr Caitlin Cottrill and Aberdeen Climate Action director Alison Stuart.
Transport minister Humza Yousaf, in a statement previously issued several times, said: “The Scottish Government continues to increase investment in active [walking and cycling] and sustainable transport.
"We have invested over Â£217 million in active travel since the start of the 2011 spending review and, as announced in the Programme for Government, we have doubled the active travel budget from around Â£40m to Â£80m a year from 2018-2019.
“Our focus will be on making our towns and cities safer and friendlier with more segregated infrastructure, where appropriate, improvements to the public realm and putting people before motorised vehicles."