One man was arrested in Oswestry on Monday, and another in Telford on Thursday.
Two other men are also facing action after West Mercia Police's 'Online Child Sexual Exploitation Team' (OCSET) carried out a week of enforcement activity
The force said that officers had arrested a 33-year-old man in Oswestry on suspicion of communicating with a 13-year-old – he has been released under investigation.
A 26-year-old man from Telford was arrested, charged and remanded in custody, accused of possessing indecent images of children
The force also carried out an arrest in Worcester where a 37-year-old man is accused of claiming to be a doctor to communicate with a 12-year-old on the messaging app Kik. He has been bailed.
Officers are also investigating a 17-year-old accused of sharing indecent images on Snapchat.
The force said the investigations are continuing, and added: "In 95 per cent of cases nationally, officers seek to avoid prosecution of children who may be sharing images inadvertently or naively. The young man was offered mental health support while enquiries continue."
The officers had teamed up with the child protection charity Stop It Now! – run by The Lucy Faithfull Foundation for the enforcement campaign.
The week of enforcement activity concludes today on National Child Sexual Exploitation Awareness Day.
Detective Chief Inspector Tony Garner said: “The enforcement activity this week is just a snapshot of our ongoing work to investigate individuals sexually exploiting children online or in person.
“We send a strong message to any offender – you cause terrible harm to children, you are not safe online and you may be the next person we target.
“We are here to help and support any victim. We will listen and reassure with no blame or judgement.
“And to the wider public we urge everyone to be vigilant to the dangers to children online. Please be aware and report anything suspicious.”
West Mercia Police have also encouraged people with concerns to seek support.
A statement from the force said: "Anyone who has been a victim of online child sexual abuse, or is worried they could become a victim, can call 101 or visit www.westmercia.police.uk/ro/report/.
"If you do not wish to speak to police you can contact Childline anonymously on 0800 1111, or the independent charity Crimestoppers, also anonymously, on 0800 555 111. Always dial 999 in an emergency."