16 papers have so far been given licences to print by the elected government.
Despite a military presence in parliament, Myanmar's elected government has been implementing reforms over the past two years.
AFP news agency says newsstands in Yangon saw a rush, as readers were eager to buy the non-government newspapers.
However, the cost of the papers, many priced at about 40 US cents, may be out of reach of many people.
Presenter: Sen Lam
Speaker: Sann Oo, deputy editor, The Myanmar Times
SANN OO: The first thing is that, as we have no censorship and if we go daily, we can present fresh and very good news to our readers. Another thing is there could be competition in the market too. We're planning to run a daily newspaper next month.
LAM: Next month?
SANN OO: Yes, in May.
LAM: Of the sixteen new dailies that were given licences, only four were ready to publish on the first day. Why do you think this is?
SANN OO: Yes. Because most of the other newspapers are still preparing to run a daily. Eleven weeklies announced that they will start publishing on May 3rd, so they're now in the serious preparation stage. And in terms of recruiting reporters and investing in printing technology and so on.
LAM: Are you taking in new staff as well?
SANN OO: Sure, yeah, we're now starting to recruit new reporters, and we're also investing and trying to introduce the new editorial system too.
LAM: And are you confident the new relaxation of media control will also be accompanied by a freer environment and less intimidation?
SANN OO: Yeah, I'm confident that our freedom will remain and we will have freedom in the future too. It's based on what I see around me, and since the relaxation of the censorship rules last August, I didn't hear any kind of incidents from my colleagues and also from myself.
LAM: Do you think the new media freedom might have some impact on the government-owned media as well - That they too, might show more independence in what's hopefully a more liberal environment now?
SANN OO: I'm sure the freedom of the press will have an impact on the government too. And then, I'm sure the media freedom means the media can report the mismanagement of the government and the government can listen to the media and they can correct their systems for the good of the people.
LAM: So you agree with some commentators, that this more open environment may mean private newspapers can also serve as a watchdog, for the public, that they'll keep the elected government more accountable?
SANN OO: Sure, yeah, I agree with that.
LAM: Do you think it'll have any impact on the content of your newspaper, will it change the kind of stories that you cover?
SANN OO: Well, it will not have an impact on our content. We already publish a wide range of content in our newspaper, so we may use the same content for our daily newspapers too.
LAM: You were already publishing stories that perhaps might be critical of the authorities?
SANN OO: Yes, yes, we already tried our best to publish critical stories.
LAM: So you were pushing the boundaries a bit?
SANN OO: Yes, sure, we always (tried).
LAM: Aung San Suu Kyi's NLD will also publish its own weekly paper, the D-Wave, 'D' for Democracy, later this month. Do you think many people might get to read it, given Myanmar's literacy rate - do you think it will reach many people?
SANN OO: The literacy rate is one thing - another thing is the market. That most of the private newspapers are planning to sell at the retail price of around 200 kyats, or lower than 200 kyats. One (US) dollar is compared to the 880 kyats.
LAM: So essentially, they're selling it for about US 40 cents?
SANN OO: Yes, yes, of course. That's still not okay for most of the low-income people. And so, I think most of the people cannot afford to buy the daily newspaper every day.
LAM: Is there a sense of celebration in the local media in Myanmar, with this historic move by the elected government?
SANN OO: Yes, I think most of the people are happy to see the first daily private newspapers. And I heard that all of the papers are sold out today.